In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:‖f (x) + f (y) + 2f (z) + 2f (w)‖ ≤‖ 2f x + y2 + z + w ‖(0.1)This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:‖f (x) + f (y) + 2f (z) + 2f (w)‖ ≤‖ 2f x + y2 + z + w ‖(0.1)This is applied to investigate isomorphisms between C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras and JC*-algebras, associated with the Cauchy-Jensen functional equation 2f (x + y/2 + z + w) = f(x) + f(y) + 2f(z) + 2f(w).展开更多
The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that thes...In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation.展开更多
Let A be a commutative C^* -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to Co(G), the C^*-algebra of all complex continuous functions on G vanishing at...Let A be a commutative C^* -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to Co(G), the C^*-algebra of all complex continuous functions on G vanishing at infinity. The result is generalized to the ease of Hopf C^*-algebra, where G is altered by a locally compact group. Using the isomorphic representation, the counit ε and the antipode S of a commutative Hopf C^*-algebra are proposed.展开更多
This paper presents the BCL+-algebras, which is derived the fundamental properties. Results are generalized with version of BCL-algebras [5], using some unusual for a binary relation * and a constant 1 (one) in a non-...This paper presents the BCL+-algebras, which is derived the fundamental properties. Results are generalized with version of BCL-algebras [5], using some unusual for a binary relation * and a constant 1 (one) in a non-empty set X, one may take different axiom systems for BCL+-algebras.展开更多
Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal ...Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm.展开更多
We investigate realization of the infinite-dimensional 3-algebras in the classical Calogero-Moser model. In terms of the Lax matrix of the Calogero Moser model and the Nambu 3-brackets in which the variables are the c...We investigate realization of the infinite-dimensional 3-algebras in the classical Calogero-Moser model. In terms of the Lax matrix of the Calogero Moser model and the Nambu 3-brackets in which the variables are the coordinates qi, and canonically conjugate momenta pi and the coupling parameter β are an extra auxiliary phase-space parameter, we present the realization of the Virasoro-Witt, w∞ and SDi f f (T2) 3-algebras, respectively.展开更多
In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth mani...In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth manifold M, and a Lie 2-algebra which is a “categorified” version of a Lie algebra. We prove that the higher-order Courant algebroids give rise to a semistrict Lie 2-algebra, and we prove that the higher-order Dorfman algebroids give rise to a hemistrict Lie 2-algebra. Consequently, there is an isomorphism from the higher-order Courant algebroids to the higher-order Dorfman algebroids as Lie 2-algebras homomorphism.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
Let H be a finite Hopf C^* -algebra and H′be its dual Hopf algebra. Drinfeld's quantum double D(H) of H is a Hopf^*-algebra. There is a faithful positive linear functional θ on D(H). Through the associated Ge...Let H be a finite Hopf C^* -algebra and H′be its dual Hopf algebra. Drinfeld's quantum double D(H) of H is a Hopf^*-algebra. There is a faithful positive linear functional θ on D(H). Through the associated Gelfand-Naimark-Segal (GNS) representation, D(H) has a faithful^* -representation so that it becomes a Hopf C^* -algebra. The canonical embedding map of H into D(H) is isometric.展开更多
The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which...The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all(∈, ∈∨q_k)-fuzzy filters on a given R_0-algebra, under the partial order, forms a complete distributive lattice.展开更多
We review on Zariski 3-algebra model of M-theory. The model is obtained by Zariski quantization of a semi-light-cone supermembrane action. The model has manifest N=1 supersymmetry in eleven dimensions and its relation...We review on Zariski 3-algebra model of M-theory. The model is obtained by Zariski quantization of a semi-light-cone supermembrane action. The model has manifest N=1 supersymmetry in eleven dimensions and its relation to the supermembrane action is clear.展开更多
We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra ass...We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra associated with the U(N) Lie algebra. There is no ghost related to the Lorentzian signature in this model. It is invariant under 64 supersymmetry transformations although the supersymmetry algebra does not close. From the model, we derive the BFSS matrix theory and the IIB matrix model in a large N limit by taking appropriate vacua.展开更多
The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital C^(*)-alg...The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital C^(*)-algebra A with the cancellation property,strict comparison and nonempty tracial state space,any four unitaries u1,u2,u3,w∈A such that(1)■,wujw-1=uj-1,w2=1A for j,k=1,2,3;(2)τ(aw)=0 and■for all n∈N,all a∈C^(*)(u1,u2,u3),j,k=1,2,3 and all tracial statesτon A,where C^(*)(u1,u2,u3)is the C^(*)-subalgebra generated by u1,u2 and u3,there exists a 4-tuple of unitaries■in A such that■and■for j,k=1,2,3.The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.展开更多
We show that the following properties of the C*-algebras in a class P are inherited by simple unital C*-algebras in the class of asymptotically tracially in P :(1) n-comparison,(2) α-comparison(1 ≤ α < ∞).
We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra...We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra if and only if it is a Finsler symmetric cone with an orientable extension,which is equivalent to the condition that V is,in an equivalent norm,the Hermitian part of a unital real C^(*)-algebra with the positive coneΩ.展开更多
We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an actio...We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.展开更多
First, that prime C~* -algebras with countable primitive ideals are all primitive C*-algebras is proved. Then the proof that prime C~* -algebras with property RR(A) = 0 are all primitive C~*-algebras is given.
In this paper, the mutual information between clock-controlled input and output sequences is discussed. It is proved that the mutual information is a strictly monotone increasing function of the length of output seque...In this paper, the mutual information between clock-controlled input and output sequences is discussed. It is proved that the mutual information is a strictly monotone increasing function of the length of output sequence, and its divergent rate is gaven.展开更多
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:‖f (x) + f (y) + 2f (z) + 2f (w)‖ ≤‖ 2f x + y2 + z + w ‖(0.1)This is applied to investigate isomorphisms between C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras and JC*-algebras, associated with the Cauchy-Jensen functional equation 2f (x + y/2 + z + w) = f(x) + f(y) + 2f(z) + 2f(w).
基金supported by NSFC (10871192)NSF of Hebei Province (A2010000194)
文摘The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
文摘In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation.
文摘Let A be a commutative C^* -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to Co(G), the C^*-algebra of all complex continuous functions on G vanishing at infinity. The result is generalized to the ease of Hopf C^*-algebra, where G is altered by a locally compact group. Using the isomorphic representation, the counit ε and the antipode S of a commutative Hopf C^*-algebra are proposed.
文摘This paper presents the BCL+-algebras, which is derived the fundamental properties. Results are generalized with version of BCL-algebras [5], using some unusual for a binary relation * and a constant 1 (one) in a non-empty set X, one may take different axiom systems for BCL+-algebras.
文摘Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11375119 and 11031005the Beijing Municipal Commission of Education under Grant No KZ201210028032
文摘We investigate realization of the infinite-dimensional 3-algebras in the classical Calogero-Moser model. In terms of the Lax matrix of the Calogero Moser model and the Nambu 3-brackets in which the variables are the coordinates qi, and canonically conjugate momenta pi and the coupling parameter β are an extra auxiliary phase-space parameter, we present the realization of the Virasoro-Witt, w∞ and SDi f f (T2) 3-algebras, respectively.
文摘In this paper, we study the relation of the algebraic properties of the higher-order Courant bracket and Dorfman bracket on the direct sum bundle TM⊕∧<sup>p</sup>T*M for an m-dimensional smooth manifold M, and a Lie 2-algebra which is a “categorified” version of a Lie algebra. We prove that the higher-order Courant algebroids give rise to a semistrict Lie 2-algebra, and we prove that the higher-order Dorfman algebroids give rise to a hemistrict Lie 2-algebra. Consequently, there is an isomorphism from the higher-order Courant algebroids to the higher-order Dorfman algebroids as Lie 2-algebras homomorphism.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
文摘Let H be a finite Hopf C^* -algebra and H′be its dual Hopf algebra. Drinfeld's quantum double D(H) of H is a Hopf^*-algebra. There is a faithful positive linear functional θ on D(H). Through the associated Gelfand-Naimark-Segal (GNS) representation, D(H) has a faithful^* -representation so that it becomes a Hopf C^* -algebra. The canonical embedding map of H into D(H) is isometric.
基金Supported by Higher School Research Foundation of Inner Mongolia(NJSY14283)
文摘The purpose of this paper is to further study the(∈,∈∨q_k)-fuzzy filter theory in R_0-algebras. Some new properties of(∈, ∈∨ q_k)-fuzzy filters are given. Representation theorem of(∈,∈∨q_k)-fuzzy filter which is generated by a fuzzy set is established. It is proved that the set consisting of all(∈, ∈∨q_k)-fuzzy filters on a given R_0-algebra, under the partial order, forms a complete distributive lattice.
文摘We review on Zariski 3-algebra model of M-theory. The model is obtained by Zariski quantization of a semi-light-cone supermembrane action. The model has manifest N=1 supersymmetry in eleven dimensions and its relation to the supermembrane action is clear.
文摘We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra associated with the U(N) Lie algebra. There is no ghost related to the Lorentzian signature in this model. It is invariant under 64 supersymmetry transformations although the supersymmetry algebra does not close. From the model, we derive the BFSS matrix theory and the IIB matrix model in a large N limit by taking appropriate vacua.
基金supported by the National Natural Science Foundation of China(Nos.11401256,11801219,11501249,11871342)the Scientific Research Fund of Zhejiang Provincial Education Department(No.Y202249575)the Zhejiang Provincial Natural Science Foundation of China(No.LQ13A010016)。
文摘The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital C^(*)-algebra A with the cancellation property,strict comparison and nonempty tracial state space,any four unitaries u1,u2,u3,w∈A such that(1)■,wujw-1=uj-1,w2=1A for j,k=1,2,3;(2)τ(aw)=0 and■for all n∈N,all a∈C^(*)(u1,u2,u3),j,k=1,2,3 and all tracial statesτon A,where C^(*)(u1,u2,u3)is the C^(*)-subalgebra generated by u1,u2 and u3,there exists a 4-tuple of unitaries■in A such that■and■for j,k=1,2,3.The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.
基金Supported by the National Natural Sciences Foundation of China (Grant No. 11871375)。
文摘We show that the following properties of the C*-algebras in a class P are inherited by simple unital C*-algebras in the class of asymptotically tracially in P :(1) n-comparison,(2) α-comparison(1 ≤ α < ∞).
基金supported by the Engineering and Physical Sciences Research Council,UK(Grant No.EP/R044228/1).
文摘We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra if and only if it is a Finsler symmetric cone with an orientable extension,which is equivalent to the condition that V is,in an equivalent norm,the Hermitian part of a unital real C^(*)-algebra with the positive coneΩ.
文摘We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.
文摘First, that prime C~* -algebras with countable primitive ideals are all primitive C*-algebras is proved. Then the proof that prime C~* -algebras with property RR(A) = 0 are all primitive C~*-algebras is given.
文摘In this paper, the mutual information between clock-controlled input and output sequences is discussed. It is proved that the mutual information is a strictly monotone increasing function of the length of output sequence, and its divergent rate is gaven.