On k-deficit Banach Frames. Armenian Journal of Mathematics - Kaushik, S. K.; Kumar, Raj (Armenian Journal of Mathematics, 2009)
k-deficit Banach frames have been defined and studied. It has been proved that if a Banach space has a Banach frame having k-deficit (k≥ 0), then its second conjugate space has a retro Banach frame. Also, we prove results regarding existence of k-deficit Banach frames in subspaces and super spaces of a Banach space and deduce that ^∞ does not have a k-deficit Banach frame for any k. Finally, we prove the equivalence of two statements regarding Banach frames.