STABILITY OF GENERALIZED DERIVATIONS ON HILBERT C*-MODULES ASSOCIATED WITH A PEXIDERIZED CAUCHY-JENSEN TYPE FUNCTIONAL EQUATION

In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.

A New Characterization on g-frames in Hilbert C^*-Modules

In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules（in Chinese）. Acta Math. Sinica, 2011, 54（1）: 1–8.).

The characterization of Γ-modules in terms of fuzzy soft Γ-submodules

In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.

CHAIN CONDITIONS FOR C＊-ALGEBRAS COMING FROM HILBERT C＊-MODULES

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.

Extended l＊-Module

Theory of uncertainty reasoning base on l-module of true value field,in this paper,an extended l-module was proposed,some properties and lattice measure were discussed,then the lattice integral on l-module was gained.

QED-Lie Algebra and Their £-Modules in Superconductivity

It’s created a canonical Lie algebra in electrodynamics with all the “nice” algebraic and geometrical properties of an universal enveloping algebra with the goal of can to obtain generalizations in quantum electrodynamics theory of the TQFT, and the Universe based in lines and twistor bundles to the obtaining of irreducible unitary representations of the Lie groups SO(4) ?andO(3,1) , based in admissible representations of U(1) , and SU(n)? . The obtained object haves the advantages to be an algebraic or geometrical space at the same time. This same space of ￡-modules can explain and model different electromagnetic phenomena in superconductor and quantum processes where is necessary an organized transformation of the electromagnetic nature of the space- time and obtain nanotechnologies of the space-time and their elements.

Boundedness of fractional integral operators on α-modulation spaces

In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.

C^(*)-Isomorphisms Associated with Two Projections on a Hilbert C^(*)-Module

Motivated by two norm equations used to characterize the Friedrichs angle,this paper studies C^(*)-isomorphisms associated with two projections by introducing the matched triple and the semi-harmonious pair of projections.A triple(P,Q,H)is said to be matched if is a Hilbert C^(*)-module,P and Q are projections on H such that their infimum P∧Q exists as an element of L(H),where L(H)denotes the set of all adjointable operators on H.The C^(*)-sub algebras of L(H)generated by elements in{P-P∧Q,Q-P∧Q,I}and{P,Q,P∧Q,I}are denoted by i(P,Q,H)and o(P,Q,H),respectively.It is proved that each faithful representation(π,X)of o(P,Q,H)can induce a faithful representation(π,X)of i(P,Q,H)such that π~(P−P∧Q)=π(P)−π(P)∧π(Q),π~(Q−P∧Q)=π(Q)−π(P)∧π(Q)..When(P,Q)is semi-harmonious,that is,R(P+Q) and R(2I−P−Q) are both orthogonally complemented in H,it is shown that i(P,Q,H)and i(I-Q,I-P,H)are unitarily equivalent via a unitary operator in L(H).A counterexample is constructed,which shows that the same may be not true when(P,Q)fails to be semi-harmonious.Likewise,a counterexample is constructed such that(P,Q)is semi-harmonious,whereas(P,I-Q)is not semi-harmonious.Some additional examples indicating new phenomena of adjointable operators acting on Hilbert C^(*)-modules are also provided.

Hilbert C* -模中g^-框架的新的等式和不等式

利用算子理论方法给出了Hilbert C*-模中g-框架的新的等式和不等式,所得结果包含了已知的一些结果。

Hilbert C~*-模上广义g-框架的不相交性

主要研究了Hilbert C*-模上广义g-框架的不相交性.通过分析算子得到了强不相交性、不相交性及弱不相交性的有关结论.

C3-Modules

One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.

*-Modules, co-*-modules and cotilting modules over Noetherian rings

Let R be a Noetherian ring. The projectivity and injectivity of modules over R are discussed. The concept of modules is introduced and the descriptions for co-*-modules over R are given. At last, cotilting modules over R are characterized by means of co-*-modules.

Irreducible Z＋-modules of near-group fusion ring K（Z3, 3）

The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible Z＋-modules over the near-group fusion ring K（Z3, 3） are explicitly classified. It turns out that there are only four inequivalent irreducible Z＋-modules of rank 2 and two inequivalent irreducible Z＋-modules of rank 4 over K（Z3, 3）.

准Hilbert C~*-模上的范数等式(英文)

目的为了研究‖x+y‖=‖x‖+‖y‖和毕达哥拉斯等式在准HilbertC*-模中成立的充要条件。方法采用了算子论方法进行研究。结果证明了‖x+y‖=‖x‖+‖y‖成立当且仅当存在A上的态使得(〈‖y‖x-‖x‖y,‖y‖x-‖x‖y〉)=0且(〈x,x〉)=‖x‖2或(〈y,y〉)=‖y‖2成立。也给出了准HilbertC*-模中毕达哥拉斯等式成立的充要条件。结论本文的结果对研究准HilbertC*-模中的范数等式非常有用。

Derivations on the Algebra of Operators in Hilbert C~*-Modules

Let M be a full Hilbert C＊-module over a C＊-algebra A, and let End^（.A4） be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End＊A（M） is an inner derivation, and that if A is a-unital and commutative, then innerness of derivations on ＂compact＂ operators completely decides innerness of derivations on EndA（M）. If .4 is unital （no commutativity is assumed） such that every derivation of A is inner, then it is proved that every derivation of EndA（Ln（A）） is also inner, where Ln（A） denotes the direct sum of n copies of A. In addition, in case A is unital, commutative and there exist xo,yo ∈M such that 〈xo,yo〉 = 1, we characterize the linear A-module homomorphisms on EndA（M） which behave like derivations when acting on zero products.

Takesaki-Takai Duality Theorem in Hilbert C^＊-Modules

In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).

The Characterization of a Class of Quantum Markov Semigroups and the Associated Operator-Valued Dirichlet Forms Based on Hilbert W＊-Module

In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W＊-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2 A and the set of regular quadratic forms, where A is a finite and a-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup （Tt）t∈R＋ C L（l2 A） is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L（l2 A） is the yon Neumann algebra of all adjointable module maps on l2 A.

On Quasi-Chebyshevity Subsets of Unital Banach Algebras

In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of those algebras are given including the algebras of continuous functions on compact sets. We also see some results in C＊-algebras and Hilbert C＊-modules. Next, by considering some conditions, we study Chebyshev of subalgebras in C＊-algebras.

FREE FISHER INFORMATION AND AMALGAMATED FREENESS

The notion of operator-valued free Fisher information was introduced.It is a generalization of free Fisher information which was defined by D.Voiculescu on tracial von Neumann algebras.It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness,i.e.,the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra.Cramer-Rao inequality in operator-valued settings is also obtained.

Equivalence and Duality between Subcategories of Modules

By discussing equivalence between Copres(K A) and Gen(P R), the characterization of *-modules was presented. The characterization of the duality between Cogen(U R) and Cogen( AU) was also discussed.