CERTAIN PROPERTIES ASSOCIATED WITH SCHAUDER FRAMES IN BANACH SPACES

Abstract

. Schauder frames satisfying property (I) and property (II) has been defined and studied. It has been proved that an atomic decomposition satisfies property (I) if and only if it satisfies property (II). Also, Schauder frames satisfying property ( M ) has been defined and it has been proved that, in a uniformly convex Banach space, if a Schauder frame satisfies property ( M ) , then it also satisfies property (II) (and hence property (I)). Further, we define atomic decompositions satisfying property ( B ) and prove that property ( B ) is a necessary condition for an atomic decomposition satisfying property (I). Finally, we define property ( SB ) for a Schauder frame and gave a necessary condition for it.