Annals of Mathematical Sciences and Applications

Volume 8 (2023)

Number 2

Special issue dedicated to Anthony To-Ming Lau on his 80th birthday

Guest Editors: Xiaolong Qin, Ngai-Ching Wong and Jen-Chih Yao

Approximate amenability and pseudo-amenability in Banach algebras

Pages: 309 – 320

DOI: https://dx.doi.org/10.4310/AMSA.2023.v8.n2.a6

Author

Yong Zhang (Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada)

Abstract

We survey the recent development of approximate amenability and pseudo-amenability in Banach algebras, concentrating on the relationship between the two notions. It has been conjectured that a Banach algebra with a bounded approximate identity is approximately amenable if and only if it is pseudo-amenable. So far we only have partial affirmative results concerning the conjecture. Some open problems are also posted.

Keywords

approximate diagonal, approximately inner, derivation

2010 Mathematics Subject Classification

Primary 43A10, 46Hxx. Secondary 16E40, 46H25.

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Dedicated to Professor Anthony To-Ming Lau: Happy 80th birthday!

The author is supported by NSERC grant RGPIN-2022-04137.

Received 13 January 2023

Accepted 19 January 2023

Published 26 July 2023