Invertibility of Multipliers for Continuous G-frames

TL;DR

This paper investigates the conditions under which multipliers for continuous g-Bessel families in Hilbert spaces are invertible, providing necessary and sufficient criteria for continuous g-frames.

Contribution

It introduces new necessary and sufficient conditions for the invertibility of multipliers in the context of continuous g-Bessel families and frames.

Findings

Necessary conditions for invertibility of multipliers.

Sufficient conditions for invertibility of multipliers for continuous g-frames.

Enhanced understanding of multiplier invertibility in Hilbert space frameworks.

Abstract

In this paper we study the concept of multipliers for continuous $g$-Bessel families in Hilbert spaces. We present necessary conditions for invertibility of multipliers for continuous $g$-Bessel families and sufficient conditions for invertibility of multipliers for continuous $g$-frames.