The structure of linear zero product and commutativity preservers of C*-algebras

被引：0
|
作者：
Liu, Jung-Hui [1 ]
Li, Lei [2 ]
Shi, Luoyi [3 ]
Wong, Ngai-Ching [4 ]
机构：
[1] Sanming Univ, Sch Informat Engn, 25 Jing Dong Rd, Sanming City 365004, Fujian, Peoples R China
[2] Nankai Univ, Sch Math Sci & LPMC, Tianjin 300071, Peoples R China
[3] Tiangong Univ, Sch Software, Tianjin 300387, Peoples R China
[4] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2021年 / 115卷 / 04期
关键词：
Zero product preservers; Commutativity preservers; Automatic continuity; C*-algebras; ORTHOGONALITY PRESERVERS; DISJOINTNESS PRESERVERS; AUTOMATIC-CONTINUITY; BISEPARATING MAPS; OPERATORS; MAPPINGS;
D O I：
10.1007/s13398-021-01134-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let theta : A(sa) -> B-sa be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) C*-algebras. Suppose. preserves commutativity in two directions (i.e., ab = ba if and only if theta(a)theta(b) = theta(b)theta(a)). We show that theta is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of B, and a real linear Jordan isomorphism J : A(sa) -> B-sa such that theta = hJ.
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页数：6
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