A solution of one Problem of Lindenstrauss and Rosenthal on Subspace Homogeneous and Quotient Homogeneous Banach Spaces with Application to the Approximation Problem and to the Schroeder - Bernstein Problem

2002/06/03 by Eugene Tokarev, Tokarev, Eugene
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Fixed Point Theorems Analysis #math.FA #msc:46A20 #msc:46B07 #msc:46B10 #msc:46B20 #msc:46B28

paper · pdf · doi:10.48550/arxiv.math/0206013

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arxiv created 2002/06/03 · arxiv updated 2009/11/30

Abstract

In article is constructed a wide couple of pairwice non-isomorphic separable superreflexive Banach spaces E that are subspace homogeneous. Their conjugates are quotient homogeneous. None of this couple neither isomorphic to its Cartesian square nor has the approximation property. At the same time, any such E is isomorphic to E+ E+ W for some Banach space W and, hence, solves the Schroeder - Bernstein problem.

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