Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate semi-amenability of Banach algebras   Let $\mathfrak{A}$ be a Banach algebra, and $\mathcal{X}$ a Banach
$\mathfrak{A}$-bimodule. A bounded linear mapping
$\mathcal{D}:\mathfrak{A}\rightarrow \mathcal{X}$ is approximately semi-inner
derivation if there eixist nets $(\xi_{\alpha})_{\alpha}$ and
$(\mu_{\alpha})_{\alpha}$ in $\mathcal{X}$ such that, for each
$a\in\mathfrak{A}$,
$\mathcal{D}(a)=\lim_{\alpha}(a.\xi_{\alpha}-\mu_{\alpha}.a)$. $\mathfrak{A}$
is called approximately semi-amenable if for every Banach
$\mathfrak{A}$-bimodule $\mathcal{X}$, every
$\mathcal{D}\in\mathcal{Z}^{1}(\mathfrak{A},\mathcal{X}^{*})$ is approximtely
semi-inner. There are some Banach algebras which are approximately
semi-amenable, but not approximately amenable. In this manuscript, we
investigate some properties of approximate semi-amenability of Banach algebras.
Also in Theorem \ref{ee} we prove the approximate semi-amenability of Segal
algebras on a locally compact group $G$.

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The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph