Embedding C*-Algebras Into the Calkin Algebra-Reference-Cited by-同舟云学术

Embedding C*-Algebras Into the Calkin Algebra

Published:2019-04-03 Issue:11 Volume:2021 Page:8188-8224
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Farah Ilijas¹,Katsimpas Georgios¹,Vaccaro Andrea²

Affiliation:

1. Department of Mathematics and Statistics, York University, 4700 Keelee Street, North York, Ontario, Canada

2. Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, Pisa, Italy

Abstract

Abstract We prove that, under Martin’s axiom, every ${\mathrm{C}}^\ast $-algebra of density character less than continuum embeds into the Calkin algebra. Furthermore, we show that it is consistent with Zermelo-Fraenkel set theory plus the axiom of choice, ZFC, that there is a $\mathrm{C}^\ast $-algebra of density character less than continuum that does not embed into the Calkin algebra.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2021/11/8188/42309313/rnz058.pdf

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