Bulletin of the Belgian Mathematical Society - Simon Stevin

Pointwise amenability for dual Banach algebras

Mannane Shakeri and Amin Mahmoodi

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Abstract

We shall develop two notions of pointwise amenability, namely pointwise Connes amenability and pointwise $w^*$-approximate Connes amenability, for dual Banach algebras which take the $w^*$-topology into account. We shall study these concepts for the Banach sequence algebras $\ell^1(\omega)$ and the weighted semigroup algebras $ \ell^{1}(\mathbb{N}_{\wedge},\omega)$. For a weight $\omega$ on a discrete semigroup $S$, we shall investigate pointwise amenability/Connes amenability of $\ell^1(S,\omega)$ in terms of diagonals.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 3 (2018), 393-401.

Dates
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1536631234

Digital Object Identifier
doi:10.36045/bbms/1536631234

Mathematical Reviews number (MathSciNet)
MR3852675

Zentralblatt MATH identifier
06970021

Subjects
Primary: pointwise amenability pointwise Connes amenability Beurling algebras

Keywords
$(H,G)$-coincidence $G$-action

Citation

Shakeri, Mannane; Mahmoodi, Amin. Pointwise amenability for dual Banach algebras. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 3, 393--401. doi:10.36045/bbms/1536631234. https://projecteuclid.org/euclid.bbms/1536631234


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