Some points on c-K-g-frames and their duals

TL;DR

This paper explores new properties of c-K-g-frames in Hilbert spaces, characterizes their duals, establishes their equivalence with atomic cg-systems, and constructs new atomic cg-systems from existing ones.

Contribution

It introduces novel properties and characterizations of c-K-g-frames and their duals, and proves the equivalence with atomic cg-systems, expanding the theoretical framework.

Findings

c-K-g-frames have new properties

Duals of c-K-g-frames are characterized

c-K-g-frames are equivalent to atomic cg-systems

Abstract

In this paper we study some new properties of c-K-g-frames in a Hilbert space H. We study duals of c-K-g-frames and give some characterizations of c-K-g-frames and their duals. Also, we verify the relationships between c-K-g-frames and atomic cg-systems. Precisely, we show that these two concepts are equivalent. Finally, we find some new atomic cg-systems from given ones.