In this paper, $X$ is a locally compact Hausdorff space and ${\mathcal A}$ is a Banach algebra. First, we study some basic features of $C_0(X,\mathcal A)$ related to $\rm BSE$ concept, which are gotten from ${\mathcal A}$. In particular, we prove that if $C_0(X,\mathcal A)$ has the $\rm BSE$ property then $\mathcal A$ has so. We also establish the converse of this result, whenever $X$ is discrete and $\mathcal A$ has the BSE-norm property. Furthermore, we prove the same result for the $\rm BSE$ property of type I. Finally, we prove that $C_0(X,{\mathcal A})$ has the BSE-norm property if and only if $\mathcal A$ has so.
Fatemeh Abtahi
,
Ali Rejali
,
Farshad Sayaf
. THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS*[J]. Acta mathematica scientia, Series B, 2024
, 44(5)
: 1945
-1954
.
DOI: 10.1007/s10473-024-0518-z
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