Invertibility preserving mappings onto finite C*-algebras

Martin Mathieu; Francois Schulz

doi:10.4064/sm230101-27-3

Invertibility preserving mappings onto finite C*-algebras

Martin Mathieu, Francois Schulz

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

2 Downloads (Pure)

Abstract

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.

Original language	English
Number of pages	7
Journal	Studia Mathematica
Early online date	26 May 2023
DOIs	https://doi.org/10.4064/sm230101-27-3
Publication status	Early online date - 26 May 2023

Bibliographical note

7 pages

Keywords

math.OA
math.FA
47B48, 47A10, 46L05, 46L30, 16W10, 17C65

Access to Document

10.4064/sm230101-27-3Licence: Unspecified

Mathieu-Schulz-1-early_online
© Instytut Matematyczny PAN 2023 This is an accepted manuscript distributed under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Accepted author manuscript, 389 KBLicence: Unspecified

Cite this

@article{b6eb61be676c4143a7a77af77adf4837,

title = "Invertibility preserving mappings onto finite C*-algebras",

abstract = "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.",

keywords = "math.OA, math.FA, 47B48, 47A10, 46L05, 46L30, 16W10, 17C65",

author = "Martin Mathieu and Francois Schulz",

note = "7 pages",

year = "2023",

month = may,

day = "26",

doi = "10.4064/sm230101-27-3",

language = "English",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Instytut Matematyczny",

}

TY - JOUR

T1 - Invertibility preserving mappings onto finite C*-algebras

AU - Mathieu, Martin

AU - Schulz, Francois

N1 - 7 pages

PY - 2023/5/26

Y1 - 2023/5/26

N2 - 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.

AB - 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.

KW - math.OA

KW - math.FA

KW - 47B48, 47A10, 46L05, 46L30, 16W10, 17C65

U2 - 10.4064/sm230101-27-3

DO - 10.4064/sm230101-27-3

M3 - Article

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

ER -

Invertibility preserving mappings onto finite C*-algebras

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this