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Ulam stability for some classes of C*-algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  10 April 2018

Paul McKenney  and
Alessandro Vignati
Paul McKenney
Affiliation:
Department of Mathematics, Miami University, 501 E. High Street, Oxford, OH 45056, USA
Alessandro Vignati
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada (ale.vignati@gmail.com)
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Abstract

We prove some stability results for certain classes of C*-algebras. We prove that, whenever A is a finite-dimensional C*-algebra, B is a C*-algebra and ϕ: A → B is approximately a *-homomorphism, there is an actual *-homomorphism close to ϕ by a factor depending only on how far ϕ is from being a *-homomorphism and not on A or B.

Keywords

Ulam stabilityC*-algebrasapproximate morphismsAF algebras

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L10: General theory of von Neumann algebras
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 1 , February 2019 , pp. 45 - 59
Copyright
Copyright © Royal Society of Edinburgh 2018 

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