Bounded operators and complemented subspaces of Cartesian products
Djakov, Plamen Borissov and Terzioğlu, Tosun and Yurdakul, Murat and Zakharyuta, Vyacheslav (2011) Bounded operators and complemented subspaces of Cartesian products. Mathematische Nachrichten, 284 (2-3). pp. 217-228. ISSN 0025-584X
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Official URL: http://dx.doi.org/10.1002/mana.200810066
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 E1 × E2, where E1 is a complemented subspace of X and E2 is a complemented subspace of Y.
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