On Geometry of Banach Spaces with Property a

W. Schachermayer showed that even 1-complemented subspaces of Banach spaces with property a can fail this property. However, we prove in this paper that spaces with property a satisfy an hereditary property. We obtain, as a conse- quence, that spaces with properties a and H. cannot be reflexive and, therefore, these spaces should contain almost isometric copies of spaces of lq1 -type. Further geometrical results on Banach spaces with both properties are also obtained.