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Cohomology groups of a new class of Kadison-Singer algebras 被引量:1
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作者 Guangyu An Xing Cheng Jun Sheng 《Science China Mathematics》 SCIE CSCD 2024年第3期593-606,共14页
Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑^(∞)_(n=1)en/2n be a separating vector for the commutant N',E_(ξ)be the projection from H onto the subspace[Cξ]spanned ... Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑^(∞)_(n=1)en/2n be a separating vector for the commutant N',E_(ξ)be the projection from H onto the subspace[Cξ]spanned by the vectorξ,and Q be the projection from K=H⊕H⊕H onto the closed subspace{(η,η,η)^(T):η∈H}.Suppose that L is the projection lattice generated by the projections(E_(ξ) 0 0 0 0 0 0 0 0),{(E 0 0 0 0 0 0 0 0):E∈N},(I 0 0 0 I 0 0 0 0) and Q.We show that L is a Kadison-Singer lattice with the trivial commutant.Moreover,we prove that every n-th bounded cohomology group H~n(AlgL,B(K))with coefficients in B(K)is trivial for n≥1. 展开更多
关键词 kadison-singer algebra kadison-singer lattice DERIVATION cohomology group
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Cohomology of a class of Kadison-Singer algebras 被引量:3
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作者 HOU ChengJun Institute of Operations Research, Qufu Normal University, Rizhao 276826, China 《Science China Mathematics》 SCIE 2010年第7期1824-1836,共13页
Let L be the complete lattice generated by a nest N on an infinite-dimensional separable Hilbert space H and a rank one projection P ξ given by a vector ξ in H. Assume that ξ is a separating vector for N , the core... Let L be the complete lattice generated by a nest N on an infinite-dimensional separable Hilbert space H and a rank one projection P ξ given by a vector ξ in H. Assume that ξ is a separating vector for N , the core of the nest algebra Alg(N ). We show that L is a Kadison-Singer lattice, and hence the corresponding algebra Alg(L) is a Kadison-Singer algebra. We also describe the center of Alg(L) and its commutator modulo itself, and show that every bounded derivation from Alg(L) into itself is inner, and all n-th bounded cohomology groups H n (Alg(L), B(H)) of Alg(L) with coefficients in B(H) are trivial for all n≥1. 展开更多
关键词 kadison-singer algebra kadison-singer lattice NEST algebra COHOMOLOGY group
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THE BSE PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS
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作者 Fatemeh ABTAHI Ali REJALI Farshad SAYAF 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1945-1954,共10页
In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the ... In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the BSE property then A has so.We also establish the converse of this result,whenever X is discrete and A has the BSE-norm property.Furthermore,we prove the same result for the BSE property of type I.Finally,we prove that C0(X,A)has the BSE-norm property if and only if A has so. 展开更多
关键词 BSE algebras BSE-function BSE norm multiplier algebra SEMISIMPLE without order
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Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra
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作者 Nicholas O. Okeke Murphy E. Egwe 《Advances in Pure Mathematics》 2024年第3期167-184,共18页
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound... Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) . 展开更多
关键词 Measure Groupoid Groupoid Equivalence Ergodic Action Convolution algebra von Neumann algebra Generalized Space
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BANACH ALGEBRA STRUCTURE IN DERIVATIVE HARDY SPACES
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作者 ZHANG Zhao-de LIU Jun-ming 《数学杂志》 2024年第6期485-493,共9页
In this paper,we consider the algebraic structure of derivative Hardy Spaces.By using the method of[6,12,15],we get the Duhamel product forming Banach algebra in derivative Hardy Spaces,and invertibility criterion,and... In this paper,we consider the algebraic structure of derivative Hardy Spaces.By using the method of[6,12,15],we get the Duhamel product forming Banach algebra in derivative Hardy Spaces,and invertibility criterion,and describe the extended eigenvalue of the integral operator V.We generalize the results in[1,2,6,11,16]. 展开更多
关键词 Duhamel product banach algebra extended eigenvalue
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Split-Tetraquaternion Algebra and Applications
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作者 Grégoire Lutanda Panga 《Journal of Applied Mathematics and Physics》 2024年第7期2682-2690,共9页
In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates th... In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry. 展开更多
关键词 Tetraquaternion algebra Split-Tetraquaternion algebra Split Quaternion algebra Clifford algebra
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Discussion on the Homology Theory of Lie Algebras
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作者 Lilong Kang Yu Wang Caiyu Du 《Journal of Applied Mathematics and Physics》 2024年第7期2367-2376,共10页
Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent m... Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2). 展开更多
关键词 Lie algebra Differential Sequence Differential Fractional algebra COHOMOLOGY
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The Report of Homological Algebra
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作者 Junhui Zhang 《Open Journal of Applied Sciences》 2024年第9期2749-2767,共19页
The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modu... The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modules. 展开更多
关键词 Homological algebra CATEGORY Projective and Injective Module
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Quantum Computingvia Entanglement in Geometric Algebra Approach
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作者 Alexander Soiguine 《Journal of Applied Mathematics and Physics》 2024年第2期445-457,共13页
The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers ... The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme. 展开更多
关键词 Geometric algebra Wave Functions ENTANGLEMENT Maxwell Equations Three-Dimensional Sphere
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Nonadditive Skew(Anti-)commuting Maps on Operator Algebras
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作者 Zhang Ting Feng Liqin Qi Xiaofei 《数学理论与应用》 2024年第3期83-93,共11页
In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obta... In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras. 展开更多
关键词 Commuting map Skew commuting map Anti-commuting map Operator algebra
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AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS
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作者 Safoura Rezaei ADERYANI Azam AHADI +1 位作者 Reza SAADATI Hari M.SRIVASTAVA 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期311-338,共28页
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
关键词 permuting tri-homomorphism in Banach algebra permuting tri-derivation on C*-algebra fixed point theorem Ulam-Hyers-Rassias stability aggregate special functions tri-additiveψ-functional inequality
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一些Kadison-Singer代数的例子 被引量:2
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作者 于嘉琪 李建奎 《华东理工大学学报(自然科学版)》 CAS CSCD 北大核心 2018年第6期945-949,共5页
设H是一个复的Hilbert空间。L={(0),L,M,K,H}是一个五角子空间格,满足M是L和x0的闭线性扩张,其中非零元x0属于K┴但不属于K+L。本文证明了Alg L是一个半单的Kadison-Singer代数。同时还给出两个不是套代数的CSL代数的例子,一个相似于某... 设H是一个复的Hilbert空间。L={(0),L,M,K,H}是一个五角子空间格,满足M是L和x0的闭线性扩张,其中非零元x0属于K┴但不属于K+L。本文证明了Alg L是一个半单的Kadison-Singer代数。同时还给出两个不是套代数的CSL代数的例子,一个相似于某个Kadison-Singer代数,另一个却与任何一个Kadison-Singer代数都不相似。 展开更多
关键词 CSL代数 kadison-singer代数 五角子空间格 半单代数
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一类生成M_(mn)(C)的Kadison-Singer格
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作者 李小奎 程乐乐 +1 位作者 向玉玲 陈本菊 《重庆工商大学学报(自然科学版)》 2015年第4期6-11,共6页
研究了矩阵代数Mmn(C)中不变子空间投影格生成的Von Neumann代数″;证明了是生成Mmn(C)的Kadison-Singer格;并通过格的关系图给出了的Hasses关系图.
关键词 kadison-singer kadison-singer代数 矩阵代数
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四阶矩阵代数中一类相似的Kadison-Singer格
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作者 王宁 刘倩 《周口师范学院学报》 CAS 2013年第5期29-33,共5页
通过研究四阶矩阵代数M4(C)中的不变子空间格,找到了一类生成von Neumann代数为A=M2(C)CI2的Kadison-Singer格,并证明了它们是相似的.
关键词 Kadison—Singer格 von NEUMANN代数 四阶矩阵代数 投影
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一类Kadison-Singer代数的内导子性质
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作者 程乐乐 李小奎 《宜春学院学报》 2014年第3期21-22,33,共3页
设L={0,I,Pk,Pξ,Q,Pk∨Pξ,Pk∨Q,Pξ∨Q,Pk∨Pξ∨Q:k=1,2,…,n-1}是个Kadison-Singer格。本文讨论此类KS格在矩阵M2n(C)和M2n-1(C)下的代数Alg(L),并且证明其每个线性导子在一定条件下是内的。
关键词 kadison-singer代数 导子 kadison-singer 矩阵代数 投影
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矩阵代数中一类新的Kadison-Singer格
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作者 陈改娟 任院红 +1 位作者 王宁 刘倩 《理论数学》 2012年第3期131-137,共7页
本文在矩阵代数M2(C)和M3(C)中由一个极大套和由一个分离向量决定的秩1投影生成的Kadison-Singer格及Kadison-Singer代数的基础上,将该类投影分别嵌入到矩阵代数M4(C)与M6(C)中,构造出了生成M4(C)与M6(C)的Kadison-Singer格并计算出了... 本文在矩阵代数M2(C)和M3(C)中由一个极大套和由一个分离向量决定的秩1投影生成的Kadison-Singer格及Kadison-Singer代数的基础上,将该类投影分别嵌入到矩阵代数M4(C)与M6(C)中,构造出了生成M4(C)与M6(C)的Kadison-Singer格并计算出了相应的Kadison-Singer代数。 展开更多
关键词 kadison-singer 矩阵代数 kadison-singer代数 von NEUMANN代数
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Some results on derivations of MV-algebras 被引量:1
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作者 WANG Jun-tao HE Peng-fei SHE Yan-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第1期126-143,共18页
In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations an... In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316]. 展开更多
关键词 MV-algebra DERIVATION fixed point set IDEAL Boolean algebra
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(ρ, τ, σ)-Derivations of Dendriform Algebras
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作者 Yousuf A. Alkhezi 《Applied Mathematics》 2023年第12期839-846,共8页
We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provid... We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras. 展开更多
关键词 Dendriform algebras DERIVATIONS Generalized Derivations
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Norm-Based Adaptive Coefficient ZNN for Solving the Time-Dependent Algebraic Riccati Equation
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作者 Chengze Jiang Xiuchun Xiao 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第1期298-300,共3页
Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environmen... Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environment, which current methods cannot effectively address. A normbased adaptive coefficient zeroing neural network(NACZNN) model to solve the TDARE problem is proposed. 展开更多
关键词 algebraIC EQUATION OPTIMAL
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Algebraic Properties for Molecular Structure of Magnesium Iodide
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作者 Ali N.A.Koam Ali Ahmad +1 位作者 Muhammad Azeem Muhammad Kamran Siddiqui 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第5期1131-1146,共16页
As an inorganic chemical,magnesium iodide has a significant crystalline structure.It is a complex and multifunctional substance that has the potential to be used in a wide range of medical advancements.Molecular graph... As an inorganic chemical,magnesium iodide has a significant crystalline structure.It is a complex and multifunctional substance that has the potential to be used in a wide range of medical advancements.Molecular graph theory,on the other hand,provides a sufficient and cost-effective method of investigating chemical structures and networks.M-polynomial is a relatively new method for studying chemical networks and structures in molecular graph theory.It displays numerical descriptors in algebraic form and highlights molecular features in the form of a polynomial function.We present a polynomials display of magnesium iodide structure and calculate several M-polynomials in this paper,particularly the M-polynomials of the augmented Zagreb index,inverse sum index,hyper Zagreb index and for the symmetric division index. 展开更多
关键词 Magnesium iodide M-polynomials algebraic properties of magnesium iodide algebraic formation of numerics of magnesium iodide
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