Nonlinear preserver problems on B(H)

被引：0
作者：
Jian Lian Cui
机构：
[1] University of Tsinghua,Department of Mathematical Science
来源：
Acta Mathematica Sinica, English Series | 2011年 / 27卷
关键词：
Star order; fundamental operator algebras; nest algebras; preserver problems; 47B49;
D O I：
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学科分类号：
摘要：
Let H be a complex Hilbert space of dimension greater than 2, and B(H) denote the Banach algebra of all bounded linear operators on H. For A, B ∈ B(H), define the binary relation A ≤* B by A*A = A*B and AA* = AB*. Then (B(H), “≤*”) is a partially ordered set and the relation “≤*” is called the star order on B(H). Denote by Bs(H) the set of all self-adjoint operators in B(H). In this paper, we first characterize nonlinear continuous bijective maps on Bs(H) which preserve the star order in both directions. We characterize also additive maps (or linear maps) on B(H) (or nest algebras) which are multiplicative at some invertible operator.
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页码：193 / 202
页数：9
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