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

Mustafaev G.

MATHEMATICAL NOTES, cilt.71, ss.661-666, 2002 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 71
  • Basım Tarihi: 2002
  • Doi Numarası: 10.1023/a:1015887921585
  • Dergi Adı: MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.661-666
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.