K-frames for Banach Spaces

Abstract

In order to reconstruct elements from the range of a linear bounded operator K on a separable Banach space, concepts of K-frames and K∗-atomic systems for Banach spaces are introduced, the relationship between the two is discussed, and the sufficient condition for a Banach space to have a K-frame is given. In addition, the duality of K-frames for Banach spaces is studied, the pair of K,K∗-dual Bessel sequences and the pair of approximate K,K∗-dual Bessel sequences for Banach spaces are introduced, and their important properties are discussed.