Bounded operators and complemented subspaces of Cartesian products

DJAKOV P., TERZİOĞLU A. T., YURDAKUL M. H., Zahariuta V.

MATHEMATISCHE NACHRICHTEN, vol.284, pp.217-228, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 284
  • Publication Date: 2011
  • Doi Number: 10.1002/mana.200810066
  • Journal Name: MATHEMATISCHE NACHRICHTEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.217-228
  • Middle East Technical University Affiliated: Yes

Abstract

We study the structure of complemented subspaces in Cartesian products X x Y of Kothe spaces X and Y under the assumption that every linear continuous operator from X to Y is bounded. In particular, it is proved that each non-Montel complemented subspace with absolute basis E subset of X x Y is isomorphic to a space of the form E(1) x E(2), where E(1) is a complemented subspace of X and E(2) is a complemented subspace of Y. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim