论文标题
矢量值$ l^p- $代数的BSE-Property
The BSE-property for vector-valued $L^p-$algebras
论文作者
论文摘要
令$ \ Mathcal A $为可分离的Banach代数，$ G $是本地紧凑的Hausdorff Group，$ 1 <P <\ iffty $。在本文中，我们首先提供了必要且充分的条件，在卷积产品下，$ l^p（g，\ mathcal a）$是Banach代数。然后，我们表征$ l^p（g，\ mathcal a）$的字符空间，如果$ \ nathcal a $是交换性的，而$ g $是abelian。此外，我们调查了$ l^p（g，\ mathcal a）$的bse-property $，并证明$ l^p（g，\ mathcal a）$是bse-algebra，并且仅当$ \ mathcal a $是bse-algebra和$ g $是有限的。最后，我们研究了$ l^p（g，\ mathcal a）$的bse-norm属性，并表明如果$ l^p（g，\ mathcal a）$是bse-norm代数，则$ \ nathcal a $就是这样。对于$ g $是有限的，$ \ mathcal a $是Unital的情况，我们证明了此声明的相反。
Let $\mathcal A$ be a separable Banach algebra, $G$ be a locally compact Hausdorff group and $1< p<\infty$. In this paper, we first provide a necessary and sufficient condition, for which $L^p(G,\mathcal A)$ is a Banach algebra, under convolution product. Then we characterize the character space of $L^p(G,\mathcal A)$, in the case where $\mathcal A$ is commutative and $G$ is abelian. Moreover, we investigate the BSE-property for $L^p(G,\mathcal A)$ and prove that $L^p(G,\mathcal A)$ is a BSE-algebra if and only if $\mathcal A$ is a BSE-algebra and $G$ is finite. Finally, we study the BSE-norm property for $L^p(G,\mathcal A)$ and show that if $L^p(G,\mathcal A)$ is a BSE-norm algebra then $\mathcal A$ is so. We prove the converse of this statement for the case where $G$ is finite and $\mathcal A$ is unital.
