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
Recommended Citation
MUSTAFAYEV, H. and ÜLGER, A. (1999) "A Class of Banach Algebras Whose Duals Have the Schur Property," Turkish Journal of Mathematics: Vol. 23: No. 3, Article 9. Available at: https://journals.tubitak.gov.tr/math/vol23/iss3/9
