Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $\Delta$-weak $\phi$-amenability of Banach algebras   Let $A$ be a Banach algebra and $\phi\in \Delta(A)\cup\{0\}$. We say that $A$
is $\Delta$-weak $\phi$-amenable if there exists an $m\in A^{**}$ such that
$m(\phi)=0$ and $m(\psi.a)=\psi(a)$ for each $\psi\in \Delta(A)$ and $a\in
\ker(\phi)$. It is shown that $A$ is $\Delta$-weak $\phi$-amenable if and only
if $\ker(\phi)$ has a bounded $\Delta$-weak approximate identity. We examine
this notion for some algebras over amenable locally compact groups. Also we
prove that every $\Delta$-weak $\phi$-amenable Banach algebra has a bounded
$\Delta$-weak approximate identity.

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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th