On excess of retro Banach frames (Q2331541)

There are many extensions of the notion of a frame in a Hilbert space. This paper deals with retro Banach frames. For example, if the conjugate space of a Banach space has a retro Banach frame, then the Banach space has a Banach frame (but not vice versa). Particular issue dealt with in this paper is the excess of a frame; i.e., the largest number of elements that can be removed from a frame so that the remaining elements still form a frame for the original space. The authors provide a characterization of the finite excess of a retro Banach frame, which states that the finite excess is equivalent to incompleteness of the system whenever the infinite number of elements is removed from the original frame. A sufficient condition for the infinite excess is also given.