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$B^p_r(F_n)$ HAS NO NONTRIVIAL IDEMPOTENTS

Part of: Topological algebras, normed rings and algebras, Banach algebras Abstract harmonic analysis

Published online by Cambridge University Press:  06 October 2022

YIFAN LIU Open the ORCID record for YIFAN LIU [Opens in a new window]  and
JIANGUO ZHANG Open the ORCID record for JIANGUO ZHANG [Opens in a new window]
YIFAN LIU*
Affiliation:
Research Center for Operator Algebras, School of Mathematical Sciences, East China Normal University, Shanghai 200062, PR China
JIANGUO ZHANG
Affiliation:
School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, PR China e-mail: jgzhang15@163.com
*
e-mail: fenix6b1s3@163.com
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Abstract

We show that there is no nontrivial idempotent in the reduced group $\ell ^p$-operator algebra $B^p_r(F_n)$ of the free group $F_n$ on n generators for each positive integer n.

Keywords

idempotentreduced group ℓp-operator algebrafree groupproperty (RD)q

MSC classification

Primary: 46H99: None of the above, but in this section
Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 1 , August 2023 , pp. 142 - 149
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The second author is supported by NSFC (No. 12171156).

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