A Class of Banach Algebras Whose Duals Have the Schur Property
Call a commutative Banach algebra A a g-algebra if it contains a bounded group G such that \overline{aco(G)} contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of g-algebras is quite rich. Then, for a g-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)}.
Anahtar Kelimeler:
Schur property, Segal algebras, almost periodic functionals.
A Class of Banach Algebras Whose Duals Have the Schur Property
Call a commutative Banach algebra A a g-algebra if it contains a bounded group G such that \overline{aco(G)} contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of g-algebras is quite rich. Then, for a g-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.,
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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