Banach algebras with bounded groups of generators, and the Schur property

Mustafaev G.

MATHEMATICAL NOTES, vol.71, pp.661-666, 2002 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71
  • Publication Date: 2002
  • Doi Number: 10.1023/a:1015887921585
  • Journal Name: MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.661-666
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

Recall that a Banach space X is said to have the Schur property if any weakly compact set in X is strongly compact. In this note we consider a Banach algebra A that has a bounded group of generators. Along with other results, it is proved that if A* has the Schur property, then the Gelfand space of the algebra A is a scattered set and, moreover, A* has the Radon-Nikodym property.