Bounded operators and complemented subspaces of Cartesian products


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

MATHEMATISCHE NACHRICHTEN, cilt.284, ss.217-228, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 284
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1002/mana.200810066
  • Dergi Adı: MATHEMATISCHE NACHRICHTEN
  • Sayfa Sayıları: ss.217-228

Özet

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