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On Character Space of the Algebra of BSE-functions

Journal: Sahand Communications in Mathematical Analysis (Vol.12, No. 1)

Publication Date:

Authors : ;

Page : 187-194

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

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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.

Last modified: 2019-04-28 14:10:01