Commutators with finite spectrum II

The purpose of this paper is to study derivations d, d′ defined on a Banach algebra A such that the spectrum a（[dx, d′x]） is finite for all x ∈ A. In particular we show that if the algebra is semisimple, then there exists an element a in the socle of A such that [d, d′] is the inner derivation implemented bv a.     

严格上三角矩阵李代数上的积零导子

设$F$ 为域, $n\geq 3$, $\bf{N}$$(n,\mathbb{F})$ 为域$\mathbb{F}$ 上所有$n\times n$ 阶严格上三角矩阵构成的严格上三角矩阵李代数, 其李运算为$[x,y]=xy-yx$. $\bf{N}$$(n, \mathbb{F})$ 上一线性映射$\varphi$ 称为积零导子,如果由$[x,y]=0, x,y\in \bf{N}$$(n,\mathbb{F})$,总可推出 $[\varphi(x), y]+[x,\varphi(y)]=0$. 本文证明 $\bf{N}$$(n,\mathbb{F})$上一线性映射 $\varphi$ 为积零导子当且仅当 $\varphi$ 为$\bf{N}$$(n,\mathbb{F})$ 上内导子, 对角线导子, 极端导子, 中心导子和标量乘法的和.     

可换环上一些上三角矩阵李代数的导子

设R是任意含单位元的可换环,t是R上n×n上三角矩阵组成的李代数,b是R上迹为零的n×n上三角矩阵组成的李代数,本文明确给出了t和b的导子代数.     

Hyper-Tauberian algebras and weak amenability of Figà-Talamanca-Herz algebras

We study certain commutative regular semisimple Banach algebras which we call hyper-Tauberian algebras. We first show that they form a subclass of weakly amenable Tauberian algebras. Then we investigate the basic and hereditary properties of them. Moreover, we show that if A is a hyper-Tauberian algebra, then the linear space of bounded derivations from A into any Banach A-bimodule is reflexive. We apply these results to the Figà-Talamanca-Herz algebra A_p(G) of a locally compact group G for p∈(1,∞). We show that A_p(G) is hyper-Tauberian if the principal component of G is abelian. Finally, by considering the quantization of these results, we show that for any locally compact group G, A_p(G), equipped with an appropriate operator space structure, is a quantized hyper-Tauberian algebra. This, in particular, implies that A_p(G) is operator weakly amenable.     

可换环上上三角矩阵李代数的局部自同构和局部导子

本文刻画了T_n(R)上的局部自同构和局部导子.利用关于T_n(R)的自同构和导子的主要结果和矩阵计算技巧,本文证明了T_n(R)上的每一个局部自同构是自同构,每一个局部导子是导子,这推广了文献关于T_n(R)的自同构和导子的主要结果.