Abstract
Let be a separable Banach algebra, be a locally compact group and . We first provide a necessary and sufficient condition for which is a Banach algebra, under convolution product. Then we characterize the character space of , in the case where is commutative and is abelian. Moreover, we investigate the BSE-property for and prove that is a BSE-algebra if and only if is a BSE-algebra and is finite. Finally, we study the BSE-norm property for and show that if is a BSE-norm algebra then is so. We prove the converse of this statement for the case where is finite and is a unital BSE-algebra.
Citation
Fatemeh Abtahi. Mitra Amiri. Ali Rejali. "THE BSE-PROPERTIES FOR VECTOR-VALUED -ALGEBRAS." Rocky Mountain J. Math. 54 (1) 1 - 12, February 2024. https://doi.org/10.1216/rmj.2024.54.1
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