Pointwise amenable, non-amenable Banach algebras
Sara Behnamian, Amin Mahmoodi
TL;DR
The paper demonstrates that pointwise amenability in Banach algebras does not imply overall amenability, providing a counterexample to a previously open question.
Contribution
It offers the first known example of a pointwise amenable Banach algebra that is not amenable, resolving a question posed by Dales, Ghahramani, and Loy.
Findings
Pointwise amenability does not imply amenability in Banach algebras.
Counterexample to the equivalence of pointwise and global amenability.
Addresses an open question in the theory of Banach algebras.
Abstract
It is shown that a pointwise amenable Banach algebra need not be amenable. This positively answer a question raised by Dales, Ghahramani and Loy.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Advanced Topics in Algebra