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
Abstract
In article is constructed a wide couple of pairwice nonisomorphic 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2002
 arXiv:
 arXiv:math/0206013
 Bibcode:
 2002math......6013T
 Keywords:

 Mathematics  Functional Analysis;
 46B10 (Primary) 46A20;
 46B07;
 46B20;
 46B28 (Secondary)
 EPrint:
 Latex2e