Invertibility preserving mappings onto finite C*-algebras

被引：0

作者：

Mathieu, Martin ^{[1
]}

Schulz, Francois ^{[2
]}

机构：

[1] Queens Univ Belfast, Math Sci Res Ctr, Belfast BT7 1NN, North Ireland

[2] Univ Johannesburg, Dept Math & Appl Math, Fac Sci, POB 524, ZA-2006 Auckland Pk, South Africa

来源：

STUDIA MATHEMATICA | 2023年 / 272卷 / 01期

基金：

新加坡国家研究基金会; 芬兰科学院;

关键词：

C*-algebras; tracial states; Jordan homomorphisms; invertibility preserving mappings; SPECTRUM; TRACE;

D O I：

10.4064/sm230101-27-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that every surjective unital linear mapping which preserves invertible elements from a Banach algebra onto a C*-algebra carrying a faithful tracial state is a Jordan homomorphism, thus generalising Aupetit's 1998 result for finite von Neumann algebras.

引用

页码：113 / 120

页数：8

共 50 条

[41] Additive mappings on von Neumann algebras preserving absolute values
Radjabalipour, M
LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 368 : 229 - 241
[42] Some zero product preserving additive mappings of operator algebras
Huang, Wenbo
Li, Jiankui
Pan, Shaoze
AIMS MATHEMATICS, 2024, 9 (08): : 22213 - 22224
[43] MAPPINGS PRESERVING SEGAL'S ENTROPY IN VON NEUMANN ALGEBRAS
Luczak, Andrzej
Podsedkowska, Hanna
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2019, 44 : 769 - 789
[44] On finite-sheeted covering mappings onto solenoids
Gumerov, RN
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (09) : 2771 - 2778
[45] Spectrum-preserving linear mappings between Banach algebras or Jordan-Banach algebras
Aupetit, B
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2000, 62 : 917 - 924
[46] Spectrum preserving linear mappings for scattered Jordan-Banach algebras
Maouche, A
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (11) : 3187 - 3190
[47] Additive rank-one preserving mappings on triangular matrix algebras
Bell, J
Sourour, AR
LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 312 (1-3) : 13 - 33
[48] Trace and spectrum preserving linear mappings in Jordan-Banach algebras
Aupetit, B
MONATSHEFTE FUR MATHEMATIK, 1998, 125 (03): : 179 - 187
[49] Filtration-preserving mappings and centralizers within graded Lie algebras
Bendersky, M.
Chen, G.
Churchill, R. C.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2009, 139 : 961 - 996
[50] Trace and spectrum preserving linear mappings in Jordan-Banach algebras
Bernard Aupetit
Monatshefte für Mathematik, 1998, 125 : 179 - 187

← 1 2 3 4 5 →