Abstract :
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.
