TY - JOUR
ID - 27982
TI - On Character Space of the Algebra of BSE-functions
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Fozouni, Mohammad
AD - Department of Mathematics and Statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, P.O.Box 163, Gonbad Kavous, Iran.
Y1 - 2018
PY - 2018
VL - 12
IS - 1
SP - 187
EP - 194
KW - Banach algebra
KW - BSE-function
KW - Character space
KW - Locally compact group
DO - 10.22130/scma.2017.27982
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_27982.html
L1 - https://scma.maragheh.ac.ir/article_27982_71b5e40149afa22c43b100c8a10c4984.pdf
ER -