2017/12/16 by Mohammad Fozouni, Fozouni, Mohammad
Mathematics · #46H05 #46J10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46H05 #msc:46J10
paper · pdf · doi:10.48550/arxiv.1712.05920
8 pages, To appear in "Sahand Communications in Mathematical Analysis"
arxiv created 2017/12/16 · openalex publication_date 2017/12/16 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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_\rmBSE(Δ(A)) consisting of all BSE-functions on Δ(A) where Δ(A) denotes the character space of A. Indeed, in the case that A=C0(X) where X is a non-empty locally compact Hausdroff space, we give a complete characterization of Δ(C_\rmBSE(Δ(A))) and in the general case we give a partial answer. Also, using the Fourier algebra, we show that C_\rmBSE(Δ(A)) is not a C^*-algebra in general. Finally for some subsets E of A^*, we define the subspace of BSE-like functions on Δ(A)∪ E and give a nice application of this space related to Goldstine's theorem.