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Turkish Journal of Mathematics

DOI

-

Abstract

Call a commutative Banach algebra $A$ a $\gamma$-algebra if it contains a bounded group $\Gamma$ such that $\overline{aco(\Gamma)}$ contains a multiple of the unit ball of $A$. In this paper, first by exhibiting several concrete examples, we show that the class of $\gamma$-algebras is quite rich. Then, for a $\gamma$-algebra $A$, we prove that $A^{\star}$ has the Schur property iff the Gelfand spectrum $\sum$ of $A$ is scattered iff $A^{\star}=ap(A)$ iff $A^{\star}=\overline{Span(\sum)}$.

First Page

441

Last Page

452

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