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

作     者：HAN DEGUANG Department of Mathematics, Qufa Normal University, Qufu 273165, Shandong, China. HAN DEGUANG Department of Mathematics, Qufa Normal University, Qufu 273165, Shandong, China.

作者机构：Department of Mathematics Qufa Normal University Qufu 273165 Shandong China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：1996年第17卷第2期

页      面：227-236页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of Chin 

主　　题：Nest algebra Derivation Continuity Linearity Banach space 

摘      要：This paper discusses the problem concerning the continuity and linearity of additive deriva tion of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebra algN 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 belongs to N. It is also proved that every additive derivation of a nest algebra is automatically linear if the underlying normed space is infinite dimemnsional.