On $Δ$-weak $ϕ$-amenability of Banach algebras

Javad Laali; Mohammad Fozouni

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arXiv · 1403.2162

On $Δ$-weak $ϕ$-amenability of Banach algebras

Javad Laali·Mohammad Fozouni

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Abstract

Let $A$ be a Banach algebra and $ϕ\in Δ(A)\cup\{0\}$. We say that $A$ is $Δ$-weak $ϕ$-amenable if there exists an $m\in A^{**}$ such that $m(ϕ)=0$ and $m(ψ.a)=ψ(a)$ for each $ψ\in Δ(A)$ and $a\in \ker(ϕ)$. It is shown that $A$ is $Δ$-weak $ϕ$-amenable if and only if $\ker(ϕ)$ has a bounded $Δ$-weak approximate identity. We examine this notion for some algebras over amenable locally compact groups. Also we prove that every $Δ$-weak $ϕ$-amenable Banach algebra has a bounded $Δ$-weak approximate identity.

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BibTeX RIS

Javad Laali, Mohammad Fozouni. 2014-04-16. On $Δ$-weak $ϕ$-amenability of Banach algebras. https://arxiv.org/abs/1403.2162

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