Banach代数H^∞（D；X）

讨论向量值函数的Banach代数H^∞（D;X）的极大理想空间的拓扑性质和代数性质,得到了若干结果。     

实Banach代数的表示

本文研究了对任意厄米实Banach*-代数的表示理论进行系统研究. 利用对该类代数所定义的一般态空间展开讨论. 获得了该类代数上可表示泛函的一系列好的性质,进而给出了不可约表示的等价刻画.这些结果将Naimark、Gaur等人的工作进行了推广.     

Banach代数L∞(T;X)

讨论向量值函数的Banach代数L∞（T；X）的极大理想空间的拓扑性质和代数性质，得到了若干结果；给出了Banach空间H∞（D；X）中闭单位球的端点的一条性质．     

实约化理论

在Borelbar空间 (E ,B ,- )上恰当地引入如下概念:实Hilbert空间的可测场 ,矢、算子及VonNeumann (VN)代数的实可测场 :ξ(·) ,a(·) ,M (·) .由此获得相当满意的实约化理论 :实VN代数M可以表达成VN代数实可测场M (·)的直接积分M =∫ _{⁺(E ,-)} M (t)dν(t) ,而场中每个VN代数M(t)将具有较为简单的性质     

正则FI代数的若干性质

讨论正则FI代数的若干性质。在研究FI代数与Boole代数间关系的同时,给出正则FI代数与BCK代数的另一种联系方式。     

三角Banach代数的等距同构

Let (X) and (X) be Banach algebras.Let (X) be a Banach (X),(X)-module with bounded 1.Then (X) is a Banach algebra with the usual operations and the norm ‖［AOMB］‖=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.     

关于特殊的实单Lie代数D4的内共轭分类

在[2]中,我们讨论了实单Lie代数的内共轭分类问题,但对于稍为困难的特殊实单Lie代数D作为例外,没有讨论.在[3]中,我们提到了可以利用定理2[3]直接证明内共轭的分类定理,但因为篇幅关系,没有给予详细的证明.在本文中,我们将讨论D_4的内共轭分类问题,并详细证明关于Satake图解的内共轭分类定理. 设of是实单Lie代数,g~c是f的复化,Autg~c,Intg~c,分别是g~c的自同构群和内自同构群;Aut(g),Int(g)Int(g)分别是g~c的自同构群拟内自同构群和内自同构群,其他符号参看[1].     

实厄米Banach*-代数

对任意实厄米的B anach*-代数进行系统研究,即对不需任何附加条件限制的代数进行研究,讨论方法与传统的假定代数具有单位元和*-运算是连续的两个重要假定条件下的方法不同.     

MS代数的核理想

本文证明了绝对不可分的MS代数和类布尔代数的每个原理想都是核理想。     

BCK-代数的模糊代数理想

在有界可换BCK-代数上引入了Fuzzy代数理想的概念,给出了Fuzzy代数理想的某些特征,讨论了Fuzzy理想与Fuzzy代数理想的关系。最后描述了全体Fuzzy集的BCK-代数特征。     

具有连续对合运算的实Banach*代数的Jordan结构

本文讨论了实Banach*代数的Jordan结构．主要结果:第一部分指出映射到 *-半单实Banach*代数上的Jordan*同态是连续的,且其核空间是闭*理想;由映射到交换实Banach*代数上的Jordan*同态诱导的因子代数也是交换的．第二部分介绍了两个不同的锥,并讨论了他们间的关系．另外,我们得到了关于实Banach*代数*- 根基的一个新的刻画．本文是Satish Shirali的工作的实化．     

A Characterization of Homomorphisms Between Banach Algebras

We show that every unital invertibility preserving linear map from a yon Neumann algebraonto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to aproblem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simplecomplex Banach algebra onto another,we also show that the following statements are equivalent:(1)Φ is an homomorphism;(2)Φ is completely invertibihty preserving;(3)Φ is 2-invertibility preserving.     

A Characterization of Homomorphisms Between Banach Algebras

We show that every unital invertibility preserving linear map from a yon Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism; this gives an affirmative answer to a problem of Kaplansky for all yon Neumann algebras. For a unital linear map Ф from a semi-simple complex Banach algebra onto another, we also show that the following statements are equivalent: (1)Ф is an homomorphism; (2) Ф is completely invertibility preserving; (3) Ф is 2-invertibility preserving.     

Nilpotent ideals in a class of Banach algebras

We introduce the concepts of approximately complemented subspaces of normed spaces and approximately biprojective algebras. We prove that any approximately biprojective Banach algebra with left and right approximate identities does not have a nontrivial nilpotent ideal whose closure is approximately complemented.

     

More Spectral Theory in Ordered Banach Algebras

We continue our development of spectral theory for positive elements in an ordered Banach algebra. In particular we provide a suitable version of the Krein-Rutman theorem, obtain some results concerning the peripheral spectrum of a positive element and provide a characterisation of positive quasi inessential elements, in the context of an ordered Banach algebra.     

Linear maps preserving ideals of C-algebras

We show that every unital linear bijection which preserves the maximal left ideals from a semi-simple Banach algebra onto a C-algebra of real rank zero is a Jordan isomorphism. Furthermore, every unital self-adjoint linear bijection on a countably decomposable factor von Neumann algebra is maximal left ideal preserving if and only if it is a *-automorphism.

     

*-representations on Banach *-algebras

We study notions of -bounded linear functionals and represent-
able functionals on Banach *-algebras. An equivalence between these two is established for general Banach *-algebras. In particular, we characterize -bounded linear functionals on Banach *-algebras with approximate identity and isometric involution. In addition, we prove a result on representation of -bounded positive linear functionals in terms of cyclic vectors for the corresponding *-representation.

     

On the Derivations of Semiprime Rings and Noncommutative Banach Algebras

Abstract Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A→A such that [D(x), x]D(x)[D(x),x] ∈ rad(A) for all x∈A. In this case, D(A) ⊆ rad (A). The author has been supported by Kangnung National University, Research Fund, 1998     

On a Filtered Multiplicative Bases of Group Algebras II

We give an explicit list of all p-groups G with a cyclic subgroup of index p ², such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis. We also prove that such a K-basis does not exist for the group algebra KG, in the case when G is either a non-Abelian powerful p-group or a two generated p-group (p2) with a central cyclic commutator subgroup. This paper is a continuation of the paper which appeared in Arch. Math. (Basel) 74 (2000), 217–285.     

Banach * 代数

Ｖ．Ｐｔáｋ［１］在有单位元的情形下详细研究了Ｂａｎａｃｈ代数．本文将推广他的结果到一般情形．特别，我们引入了可正开拓的正线性泛函，并对它进行了刻划．