Embedding C*-algebras into the Calkin algebra

Ilijas Farah; Georgios Katsimpas; Andrea Vaccaro

doi:10.1093/imrn/rnz058

Embedding C^*-algebras into the Calkin algebra

Ilijas Farah, Georgios Katsimpas, Andrea Vaccaro

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

7 Scopus citations

Abstract

We prove that, under Martin’s axiom, every C^*-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 C^*-algebra of density character less than continuum that does not embed into the Calkin algebra.

Original language	English
Pages (from-to)	8188-8224
Number of pages	37
Journal	International Mathematics Research Notices
Volume	2021
Issue number	11
DOIs	https://doi.org/10.1093/imrn/rnz058
State	Published - 1 Jan 2019
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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title = "Embedding C*-algebras into the Calkin algebra",

abstract = "We prove that, under Martin{\textquoteright}s axiom, every C*-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 C*-algebra of density character less than continuum that does not embed into the Calkin algebra.",

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AB - We prove that, under Martin’s axiom, every C*-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 C*-algebra of density character less than continuum that does not embed into the Calkin algebra.

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Embedding C^*-algebras into the Calkin algebra

Abstract

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