A generalization of frames in Banach spaces

Fusion Banach frames satisfying property S have been studied. A sufficient condition for the existence of a fusion Banach frame satisfying property S in weakly compactly generated Banach spaces has been given. Also, a necessary and sufficient condition for a fusion Banach frame to satisfy property S has been given. Finally, fusion Banach frames satisfying property S have been characterized in terms of closedness of certain subspaces of the dual spaces in the weak*-topology.