自反算子代数的导子和同构

本文证明了：Ｂａｎａｃｈ空间上完全分配格代数间的导子都是自动连续的；进而证明了套代数的可加导子是内的，套代数间的代数同构是自动连续的、空间的     

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.     

Nonlinear Jordan Higher Derivations of Triangular Algebras

In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algeb...     

Derivations of noncommutative Arens algebras

The present paper deals with derivations of noncommutative Arens algebras. We prove that every derivation of an Arens algebra associated with a von Neumann algebra and a faithful normal finite trace is inner. In particular, each derivation on such algebras is automatically continuous in the natural topology, and in the commutative case, even for semi-finite traces, all derivations are identically zero. At the same time, the existence of noninner derivations is proved for noncommutative Arens algebras with a semi-finite but nonfinite trace.     

Continuity of generalized derivations on JB*-algebras

We prove that every generalized Jordan derivation D from a JB?-algebra 𝒜 into itself or into its dual space is automatically continuous. In particular, we establish that every generalized Jordan derivation from a C?-algebra to a Jordan Banach module is continuous. As a consequence, every generalized derivation from a C?-algebra to a Banach bimodule is continuous.     

套代数上的Jordan导子

本文主要研究套代数上的Ｊｏｒｄａｎ导子．证明了套代数上的任一Ｊｏｒｄａｎ导子都是内导子；作为应用最后讨论了套代数上的Ｊｏｒｄａｎ自同构．     

套代数上的可加双导子和中心化映射

令$\mathcal N$是Banach空间$X$上的套, Alg$\mathcal N$是相应的套代数. 本文证明了, 如果套$\mathcal N$中存在非平凡元$N$在$X$中可补, 且$\dim N\not=1$, 则Alg$\mathcal N$上的每个可加双导子是内导子. 作为此定理的应用, 分别给出了套代数上中心化(交换)映射, 斜中心化导子以及斜交换的广义导子的具体刻画.     

Von Neumann代数中的套子代数

本文主要讨论因子Ｖｏｎ Ｎｅｕｍａｎｎ代数中套子代数上的线性满等距和自伴导子．证明了因子Ｖｏｎ Ｎｅｕｍａｎｎ代数中套子代数上的每个线性满等距是同构乘酉算子或者是反同构乘酉算子；给出了其上自伴导子是内导子的条件并得到有限因子 Ｖｏｎ Ｎｅｕｍａｎｎ代数中套子代数上的每个自伴导子都是内导子．     

某些算子代数的可加导子

本文主要研究非Ｉｎ型因子ＶｏｎＮｅｕｍａｎｎ代数的Ｎｅｓｔ子代数及两元生成格自反代数的可加导子的自动线性性和连续性问题．通过给出一个含无限维交换ＶｏｎＮｅｕｍａｎｎ子代数的代数上可加导子定理，证明了非Ｉｎ型因子ＶｏｎＮｅｕｍａｎｎ代数的Ｎｅｓｔ子代数上的可加导子是线性的，从而是自动连续的．这推广并简化证明了作者［１］中的主要结果．对于在非自伴算子代数研究中起重要的两元生成格自反代数，给出了所有可加导子是线性导子的充分必要条件．     

Linear Maps Preserving the Closure of Numerical Range on Nest Algebras with Maximal Atomic Nest

Let be a maximal atomic nest on Hilbert space H and denote the associated nest algebra. We prove that a weakly continuous and surjective linear map preserves the closure of numerical range if and only if there exists a unitary operator such that for every or for every , where denotes the transpose of T relative to an arbitrary but fixed base of H. As applications, we get the characterizations of the numerical range or numerical radius preservers on . The surjective linear maps on the diagonal algebras of atomic nest algebras preserving the closure of numerical range or preserving the numerical range (radius) are also characterized. Submitted: January 3, 2001?Revised: December 2, 2001     

一类模李代数的导子代数(英文)

本文通过构造一类模线状李代数,求出了它的导子代数,并且证明这个导子代数是可解但不完备的模李代数.这将有利于研究一般模线状李代数的结构.     

Extreme points in triangular UHF algebras

We examine the strongly extreme point structure of the unit balls of triangular UHF algebras. The semisimple triangular UHF algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal. In contrast to this, for the class of full nest algebras we prove a Krein-Milman type theorem which asserts that every operator in the open unit ball of the algebra is a convex combination of strongly extreme points.

     

Genetic Volterra algebras and their derivations

The present paper is devoted to genetic Volterra algebras. We first study characters of such algebras. We fully describe associative genetic Volterra algebras, in this case all derivations are trivial. In general setting, i.e., when the algebra is not associative, we provide a su?cient condition to get trivial derivation on generic Volterra algebras. Furthermore, we describe all derivations of three dimensional generic Volterra algebras, which allowed us to prove that any local derivation is a derivation of the algebra.     

套代数上高阶导子的刻画

设N是Banach空间X上的套,AlgN是相应的套代数。本文证明了,若套N中存在一个非平凡元在X中可补,那么AlgN上的每个可加Jordan高阶导子和每个可加三重Jordan高阶导子都是高阶导子。     

Derivations and nest algebras on Banach space

In this paper the notions of nest and nest algebra are generalised to sets of operators on Banach space. Their fundamental properties are established and continuous derivations on such algebras are shown to be implemented by an operator which can be constructed explicitly.     

Interpolation of Banach algebras and tensor products of Banach couples

Using tensor products of Banach couples we study a class of interpolation functors with the property that to every Banach couple of Banach algebras they give an interpolation space which is a Banach algebra. For the real θ,1-method we give a complete answer to the question of when the interpolation space is unital.     

New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations

We introduce a class of Banach algebras satisfying certain sequential condition (P) and we prove fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators. Later on, we give some examples of applications of these types of results to the existence of solutions of nonlinear integral equations in Banach algebras.     

实Nest代数上的广义Jordan~*-左导子

设H是实Hilber空间, (?)是B(H)中含恒等算子I的算子代数,若(?) 是从(?)到B(H)的线性映射,如果(?)满足对任意的T∈(?),有(?)(T2)=T*(?)(T)+ (?)(T)T-T*(?)(I)T,则称(?)是一个广义Jordan*-左导子;如果(?)满足对任意的T∈(?), 有(?)(T)(ker(T))(?)ran(T*),则称(?)是一个左*-核值保持映射.本文主要获得了如下 结果: Nest代数上每个弱算子拓扑连续的左*-核值保持映射是广义Jordan*-左内 导子,即存在A,B∈B(H),使得对任意的T∈(?),有(?)(T)=T*A+BT.特别地,(?) 也是一个广义Jordan*-左导子.