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Bounded operators and complemented subspaces of Cartesian products

2011-02-01
DJAKOV, PLAMEN
TERZİOĞLU, AHMET TOSUN
Yurdakul, Murat Hayrettin
Zahariuta, V.
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