ON GEOMETRY OF BANACH-SPACES WITH PROPERTY-ALPHA

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.