Construction of k-g-fusion frames and their duals in Hilbert spaces

TL;DR

This paper introduces k-g-fusion frames in Hilbert spaces, explores their duals, identities, construction methods, and stability under perturbations, extending the theory of fusion and generalized frames with applications in sampling.

Contribution

It defines and characterizes k-g-fusion frames, discusses duals and Q-duals, and provides construction and stability results, advancing the understanding of generalized fusion frames in Hilbert spaces.

Findings

Characterization of k-g-fusion frames

Methods for constructing k-g-fusion frames

Stability results under perturbations

Abstract

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion frames for operators aka k-g-fusion frames and we get some results for characterization of these frames. We further discuss on duals and Q-duals in connection with k-g-fusion frames. Also we obtain some useful identities for these frames. We also give several methods to construct k-g-fusion frames. The results of this paper can be used in sampling theory which are developed by g-frames and especially fusion frames. In the end, we discuss the stability of a more general perturbation for k-g-fusion frames.