Bounded operators and complemented subspaces of Cartesian products
MATHEMATISCHE NACHRICHTEN, vol.284, pp.217-228, 2011 (SCI-Expanded, Scopus)
- 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