论文标题
$ c^{*} $ - 矢量值Banach代数的属性
$C^{*}$- properties of vector-valued Banach algebras
论文作者
论文摘要
令$ x $为本地紧凑的豪斯多夫空间，而$ a $是标量场上$ \ mathbb {c} $上的交换性半完整的Banach代数。评估了不同类型的BSE Banach代数$ A $与Banach代数$ C_ {0}（x，a）$之间的相关性。发现并批准$ c_ {0}（x，a）$是$ c^{*} $ - 代数时，并且仅当$ a $是这样。此外，$ c_ {b}（x，a）= c_ {0}（x，a）$，仅当$ x $紧凑。
Let $X$ be a locally compact Hausdorff space, and $A$ be a commutative semisimple Banach algebra over the scalar field $\mathbb{C}$. The correlation between different types of BSE- Banach algebras $A$, and the Banach algebra $C_{0}(X, A)$ are assessed. It is found and approved that $C_{0}(X, A)$ is a $C^{*}$- algebra if and only if $A$ is so. Furthermore, $C_{b}(X, A)= C_{0}(X, A)$ if and only if $X$ is compact.
