J4 ›› 2013, Vol. 48 ›› Issue (10): 1-4.

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Characterizations of Jordan isomorphism on standard operator algebras

ZHAO Jie-ling, ZHANG Jian-hua   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2012-12-29 Published:2013-10-14

Abstract:

Let A and B be standard operator algebras on an infinite dimensional Banach space X and ψ: A→B be a preserve unit linear bijection. We prove that if ψ(A。B)=ψ(A)。ψ(B) holds for all A,B∈A with AB=0, then for all A,B∈A either ψ(AB)=ψ(A)ψ(B) or ψ(AB)=ψ(B)ψ(A) holds.

Key words: standard operator algebra; Jordan isomorphism; isomorphism

CLC Number: 

  • O177.1
[1] PENG Dong-xia, ZHANG Jian-hua. Characterizations of a pair of generalized derivations on nest algebras [J]. J4, 2013, 48(10): 5-8.
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