K-g-frames and approximate K-g-duals in Hilbert spaces

TL;DR

This paper extends the concept of approximate duality to K-g-frames in Hilbert spaces, introduces new K-g-frames and approximate K-g-duals, and provides conditions for subsequences of K-g-frames to remain frames.

Contribution

It generalizes approximate duality results to K-g-frames, constructs new K-g-frames and duals, and characterizes subsequences that preserve the K-g-frame property.

Findings

Established new results on approximate K-g-duals.

Constructed new K-g-frames from existing ones.

Provided conditions for subsequences to remain K-g-frames.

Abstract

Approximate duality of frame pairs have been investigated by Christensen and Laugesen in (Sampl. Theory Signal Image Process., 9, 2011, 77-90), with the motivation to obtain an important applications in Gabor systems, wavelets and general frame theory. In this paper we obtain some of the known results in approximate duality of frames to K-g-frames. We also obtain new K-g-frames and approximate K-g-duals from a K-g-frame and an approximate K-g-dual. Finally, we give an equivalent condition under which the subsequence of a K-g-frame still to be a K-g-frame.