Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The multiplier algebra and BSE-functions for certain product of Banach
  algebras   In this paper, we characterize the (left) multiplier algebra of a semidirect
product algebra ${\mathcal A}={\mathcal B}\oplus {\mathcal I}$, where
${\mathcal I}$ and ${\mathcal B}$ are closed two-sided ideal and closed
subalgebra of ${\mathcal A}$, respectively. As an application of this result we
investigate the BSE-property of this class of Banach algebras. We then for two
commutative semisimple Banach algebras ${\mathcal A}$ and ${\mathcal B}$
characterize the BSE-functions on the carrier space of ${\mathcal A}\times_\phi
{\mathcal B}$, the $\phi$-Lau product of ${\mathcal A}$ and ${\mathcal B}$, in
terms of those functions on carrier spaces of ${\mathcal A}$ and ${\mathcal
B}$. We also prove that ${\mathcal A}\times_\phi {\mathcal B}$ is a BSE-algebra
if and only if both ${\mathcal A}$ and ${\mathcal B}$ are BSE.

15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
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The categories of this paper are: stat
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph