Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

Caliskan E.

CZECHOSLOVAK MATHEMATICAL JOURNAL, cilt.57, sa.2, ss.763-776, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 2
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1007/s10587-007-0112-2
  • Dergi Adı: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.763-776
  • İstanbul Üniversitesi Adresli: Hayır

Özet

We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.