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


Creative Commons License

ÇALIŞKAN E.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.57, no.2, pp.763-776, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1007/s10587-007-0112-2
  • Journal Name: CZECHOSLOVAK MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.763-776
  • Yıldız Technical University Affiliated: Yes

Abstract

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.