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 $A^{\star}=\overline{Span(\sum)}$.
Keywords
Schur property, Segal algebras, almost periodic functionals.
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
