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A COUNTEREXAMPLE TO A RESULT OF JABERI AND MAHMOODI
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 110 / Issue 1 / August 2024
- Published online by Cambridge University Press:
- 10 August 2023, pp. 155-157
- Print publication:
- August 2024
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- Article
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We show that
$\ell ^1(\mathbb {N}_\wedge )$ is 
$\varphi $-amenable for each multiplicative linear functional 
$\varphi :\ell ^1(\mathbb {N}_\wedge )\rightarrow \mathbb {C}.$ This is a counterexample to the final corollary of Jaberi and Mahmoodi [‘On 
$\varphi $-amenability of dual Banach algebras’, Bull. Aust. Math. Soc. 105 (2022), 303–313] and shows that the final theorem in that paper is not valid.
ON
$\varphi $
-AMENABILITY OF DUAL BANACH ALGEBRAS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 105 / Issue 2 / April 2022
- Published online by Cambridge University Press:
- 09 July 2021, pp. 303-313
- Print publication:
- April 2022
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Generalising the concept of injectivity, we study the notion of
$\varphi $
-injectivity for dual Banach algebras. It provides a framework for studying 
$\varphi $
-amenability of enveloping dual Banach algebras.
