# Invertibility of generalized g-frame multipliers in Hilbert spaces

## TL;DR

This paper studies the conditions under which generalized g-frame multipliers in Hilbert spaces are invertible, providing new methods for their construction and representation, with results differing from previous research.

## Contribution

It introduces novel approaches for constructing and representing invertible generalized g-frame multipliers, expanding understanding beyond prior work.

## Key findings

- Invertibility characterized for semi-normalized symbols
- Inverse multipliers can be represented as generalized g-frame multipliers
- New methods for constructing invertible multipliers

## Abstract

In this paper, we investigate the invertibility of generalized g-Bessel multipliers. We show that for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame multiplier. Also we give several approaches for constructing invertible generalized g-frame multipliers from the given one. It is worth mentioning that some of our results are quite different from those studied in the previous literatures on this topic.