几类保持映射的刻画

CHARACTERIZATIONS OF SEVERAL CLASSES OF PRESERVERS

本文研究了一类三元组正交保持的线性映射并刻画了保持τ-可测算子谱的线性映射.我们在更弱的条件下利用性质B刻画了保持三元组正交的线性映射,获得了这类映射是广义的Jordan导子的结果.对于保持τ-可测算子谱的线性映射研究,我们将有界算子中保谱的结果推广到无界算子.

In this paper,we study a class of linear mappings that triple orthogonality preservers and characterize those linear mappings that preserve the spectrum on algebras of τ-measurable operators.First,we use the property B to characterize linear mappings that triple orthogonality preservers under slightly weaker assumptions,and obtain that such mappings are generalized Jordan derivations.For the study of linear mappings which preserve the τ-measurable operator spectrum,the result of spectrum-preserving in bounded operators is extended to un-bounded operators.