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Bounded Operators and Complemented Subspaces of Cartesian Products

✍ Scribed by P. Djakov; T. Terzioğlu; M. Yurdakul; V. Zahariuta

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
157 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We study the structure of complemented subspaces in Cartesian products X × Y of Köthe 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 ⊂ X × Y is isomorphic to a space of the form E~1~ × E~2~, where E~1~ is a complemented subspace of X and E~2~ is a complemented subspace of Y. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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