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INHERITANcE OF DIVISIBILITY FORMS A LARGE SUBALGEBRA

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Acta Mathematica Scientia 2021年第1期41卷 85-96页

作者：范庆斋方小春赵霞 Department of Mathematics Shanghai Maritime University Shanghai 201306China Department of Mathematics Tongji University Shanghai 200092China

Let A be an infinite dimensional stably finite unital simple separable c^(*)-*** B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).Then A is 2... 详细信息

关键词： c^(*)c*-algebras large subalgebra cuntz semigroup

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

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Acta Mathematica Sinica,English Series 2012年第8期28卷 1615-1622页

作者： Peng Tong LI De Guang HAN Wai Shing TANG Department of Mathematics Nanjing University of Aeronautics and Astronautics Department of Mathematics University of Central Florida Department of Mathematics National University of Singapore

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.

关键词： Derivations inner derivations c*c*-algebras Hilbert c*-modules

On Monotone Product of Operator algebras

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Acta Mathematica Sinica,English Series 2007年第3期23卷 491-496页

作者： Wen Ming WU Li Guang WANG Department of Mathematical Science University of Tsinghua Beijing 100084 P. R. China Department of Mathematics Qufu Normal University Qufu 273165 P. R. China

In this note, we give complete descriptions of the structure of the monotone product of two yon Neumann algebras and two c^＊c*-algebras. We show that the monotone product of two simple yon Neumann algebras and c^＊c*-algebras aren＇t simple again. We also show that the monotone product of two hyperfinite yon Neumann algebras is again hyperfinite and determine the type of the monotone product of two factors.

关键词： factor von Neumann algebras monotone product c^*c*-algebras GNS construction

cROSSED PRODUcTS BY FINITE GROUP AcTIONS WITH cERTAIN TRAcIAL ROKHLIN PROPERTY

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Acta Mathematica Scientia 2018年第3期38卷 829-842页

作者：范庆斋方小春 Department of Mathematics Shanghai Maritime University Department of Mathematics Tongji University

We introduce a special tracial Rokhlin property for unital c~＊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.

关键词： c~*c*-algebras Rokhlin property crossed product c~*-algebra

Automorphism group on the Toeplitz algebras

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chinese Science Bulletin 1996年第8期41卷 617-620页

作者：严从荃孙顺华 Department of Mathematics Sichuan Union University Chengdu 610064 China

Let B be the unit ball of cn, S2n-1 the unit sphere of cn. The concept of the Toeplitzoperators on Hardy space H2(S2n-1) is as usual. Denote by c(S2n-1) the algebra of all con-tinuous functions on S2n-1, and (c(S2n-1)... 详细信息

关键词： Toeplitz algebras automorphism group extensions of c*c*-algebras several complex variables.

On Quasi-chebyshevity Subsets of Unital Banach algebras

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Analysis in Theory and Applications 2018年第1期34卷 92-102页

作者： M.Iranmanesh F.Soleimany Department of Mathematical Sciences Shahrood University of Technology

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＊c*-algebras and Hilbert c＊-modules. Next, by considering some conditions, we study chebyshev of subalgebras in c＊c*-algebras.

关键词： Best approximation Quasi-chebyshev sets Pseudo-chebyshev c*c*-algebras Hilbertc*-modules.

A NON-cOMMUTATIVE GENERALIZATION OF GELFAND-NA1MARK THEOREM

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Science china Mathematics 1990年第2期33卷 156-164页

作者：李炳仁 Institute of Mathematics Academia Sinica

This paper proves that a c*-algebra is standard if and only if it is isometrically *-isomorphic to a c*-algebra defined by a continued field of primitive c*c*-algebras, so a more reasonable definition of standard c*c*-algebras is obtained. However, an example of a non-normal GcR c*-algebra is given, which solves negatively an open question presented by W. H. ching in 1976.

关键词： standard c*c*-algebras primitive c*c*-algebras continued field.

On ultraproducts of operator algebras

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Science china Mathematics 2005年第9期 134-145页

作者： LI Weihua Institute of Mathematics,Academy of Mathematics and Systems Science,chinese Academy of Sciences,Beijing 100080,china

Some basic questions on ultraproducts of c*-algebras and von Neumann al- gebras,including the relation to K-theory of c*-algebras are *** specifically, we prove that under certain conditions,the K-groups of ultraproduct of c*-algebras are iso- morphic to the ultraproduct of respective K-groups of *** also show that the ultraproducts of factors of type Ⅱare prime,*** isomorphic to any non-trivial tensor product.

关键词： von Neumann algebras c*-algebras ultraproducts K-group double commutants