Fozouni, M. (2018). On Character Space of the Algebra of BSE-functions. Sahand Communications in Mathematical Analysis, 12(1), 187-194. doi: 10.22130/scma.2017.27982
Mohammad Fozouni. "On Character Space of the Algebra of BSE-functions". Sahand Communications in Mathematical Analysis, 12, 1, 2018, 187-194. doi: 10.22130/scma.2017.27982
Fozouni, M. (2018). 'On Character Space of the Algebra of BSE-functions', Sahand Communications in Mathematical Analysis, 12(1), pp. 187-194. doi: 10.22130/scma.2017.27982
Fozouni, M. On Character Space of the Algebra of BSE-functions. Sahand Communications in Mathematical Analysis, 2018; 12(1): 187-194. doi: 10.22130/scma.2017.27982
On Character Space of the Algebra of BSE-functions
Department of Mathematics and Statistics, Faculty of Basic Sciences and Engineering, Gonbad Kavous University, P.O.Box 163, Gonbad Kavous, Iran.
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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