@article {
author = {Fozouni, Mohammad},
title = {On Character Space of the Algebra of BSE-functions},
journal = {Sahand Communications in Mathematical Analysis},
volume = {12},
number = {1},
pages = {187-194},
year = {2018},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2017.27982},
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.},
keywords = {Banach algebra,BSE-function,Character space,Locally compact group},
url = {https://scma.maragheh.ac.ir/article_27982.html},
eprint = {https://scma.maragheh.ac.ir/article_27982_71b5e40149afa22c43b100c8a10c4984.pdf}
}