# On Character Space of the Algebra of BSE-functions

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

**Publication Date**: 2018-11-01

**Authors** : Mohammad Fozouni;

**Page** : 187-194

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

### Abstract

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.

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