Continuous K-G-Frame in Hilbert Spaces

TL;DR

This paper introduces the concept of c-K-g-frames in Hilbert spaces, generalizing K-g-frames, and explores their properties, operators, conditions, and stability under perturbations.

Contribution

It presents the first definition of c-K-g-frames, establishes their fundamental properties, and analyzes their stability and operator relations in Hilbert spaces.

Findings

c-K-g-frames generalize K-g-frames

Necessary and sufficient conditions for c-K-g-frames

Perturbation stability of c-K-g-frames

Abstract

In this paper we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames on Hilbert spaces. Moreover, we define the related oprators of c-K-g frames. Then, we give necessary and sufficient conditions on c-K-frames to characterize them. Finally, we verify perturbation of c-K-g-frames.