标准算子代数上的ξ-Lie可导映射与广义ξ-Lie可导映射.docVIP

标准算子代数上的 ξ?Lie 可导映射与广义 ξ?Lie 可导映射 刘磊 , 吉国兴 陕西师范大学数学与信息科学学院, 西安 710062 摘要：设 X 是实数域或复数域 F 上的 Banach 空间, A B(X) 为标准算子代数. 本文主要证 明了当 ξ = 1 时, A 上的 ξ?Lie 可导映射 δ 为可加导子与由 A 到 F 且零化换位子的映射之和; 当 ξ ?= 1 时, δ 为可加导子且满足 δ(ξA) = ξδ(A). 关于广义 ξ?Lie 可导映射的相关问题本文也 给出了相应的结论. 关键词：标准算子代数; 导子; ξ-Lie 可导映射; 广义 ξ-Lie 可导映射 中图分类号： 177.1 ξ?Lie derivable maps and generalized ξ?Lie derivable maps on standard operator algebras Lei Liu , Guoxing Ji College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062 Abstract: Let X be a Banach space over the real or complex ?eld F and A ? B(X) be a standard operator algebra. We prove that a ξ?Lie derivable map δ on A is the sum of an additive derivation and a map from A to F vanishing all commutators when ξ = 1; is an additive derivation satisfying δ(ξA) = ξδ(A) when ξ ?= 1. Related results concerning generalized ξ?Lie derivable maps are given. Key words: Standard operator algebras; Derivations; ξ-Lie derivable maps; Generalized ξ-Lie derivable maps 0 Introduction Recently, the relationships between the multiplication and the addition structures of rings and algebras are discussed by several authors. Martindale in [1] proved that multiplicative bijective maps on ring with some condition is additive. Lu in [2] proved the multiplicative 基金项目： the National Natural Science Foundation of China(No, the Specialized Research Fund for the Doctoral Program of Higher Education(No.20090202110001) 作者简介： Lei Liu, PhD student, major research direction：operator theory and operator algebras. Correspondence author：Guoxing Ji, professor, major research direction：operator theory and operator algebras. -1- bijective maps on nest algebras is additive. Wang in [3] proved the similar result on triangular rings. For Jordan product, paper [4] proved if A is a standard operator algebra on a Banach space of dimension at least 2, then every bijective Jordan multiplicative maps form A onto another ring is additive. An in [5] characterized the Jorda