ON GEOMETRY OF BANACH-SPACES WITH PROPERTY-ALPHA

Authors
Citation
Jp. Moreno, ON GEOMETRY OF BANACH-SPACES WITH PROPERTY-ALPHA, Journal of mathematical analysis and applications, 201(2), 1996, pp. 600-608
Citations number
17
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
ISSN journal
0022247X
Volume
201
Issue
2
Year of publication
1996
Pages
600 - 608
Database
ISI
SICI code
0022-247X(1996)201:2<600:OGOBWP>2.0.ZU;2-H
Abstract
W. Schachermayer showed that even 1-complemented subspaces of Banach s paces with property alpha can fail this property. However, we prove in this paper that spaces with property alpha satisfy an hereditary prop erty. We obtain, as a consequence, that spaces with properties alpha a nd (H) cannot be reflexive and, therefore, these spaces should contain almost isometric copies of spaces of l(1)(+)-type. Further geometrica l results on Banach spaces with both properties are also obtained. (C) 1996 Academic Press, Inc.