University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101On Character Space of the Algebra of BSE-functions1871942798210.22130/scma.2017.27982ENMohammad FozouniDepartment of Mathematics and Statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, P.O.Box 163, Gonbad Kavous, Iran.Journal Article20161031Suppose 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.http://scma.maragheh.ac.ir/article_27982_71b5e40149afa22c43b100c8a10c4984.pdf