On Character Space of the Algebra of BSE-functions

Sahand Communications in Mathematical Analysis

Mohammad Fozouni¹ 

[1] Department of Mathematics and Statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, P.O.Box 163, Gonbad Kavous, Iran.;

关键词: Banach algebra;    BSE-function;    Character space;    Locally compact group;   

DOI  :  10.22130/scma.2017.27982

来源: DOAJ

【 摘 要 】

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterization of $Delta(C_{rm{BSE}}(Delta(A)))$ and in the general case we give a partial answer.  Also, using the Fourier algebra, we show that $C_{rm{BSE}}(Delta(A))$ is not a $C^*$-algebra in general. Finally for some subsets $E$ of $A^*$, we define the subspace of BSE-like functions on $Delta(A)cup E$ and give a nice application of this space related to Goldstine's theorem.

【 授权许可】

Unknown