Shadow of operators on frames

Abstract

Aldroubi introduced two methods for generating frames of a Hilbert space H. In one of his method, one approach is to construct frames for H which are images of a given frame for H under T ∈ B (H, H), a collection of all bounded linear operator on H. The other method uses bounded linear operator on ` 2 to generate frames of H. In this paper, we discuss construction of the retro Banach frames in Hilbert spaces which are images of given frames under bounded linear operators on Hilbert spaces. It is proved that the compact operators generated by a certain type of a retro Banach frame can construct a retro Banach frame for the underlying space. Finally, we discuss a linear block associated with a Schauder frame in Banach spaces.