On some dual frames multipliers with at most countable spectra

TL;DR

This paper investigates the spectral properties of dual frames multipliers in Hilbert spaces, providing conditions for their spectra to be at most countable, extending existing results on Bessel multipliers and dual Riesz bases.

Contribution

It extends the understanding of spectra of dual frames multipliers, especially regarding conditions for countability, building on prior work on Bessel multipliers and dual Riesz bases.

Findings

Identifies conditions for dual frames multipliers to have at most countable spectra

Extends spectral analysis results from Bessel multipliers to dual frames

Provides new insights into the spectral structure of dual frames multipliers

Abstract

A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the spectra of some dual frames multipliers giving, in particular, conditions to be at most countable. The contribution extends the results available in literature about the spectra of Bessel multipliers with symbol decaying to zero and of multipliers of dual Riesz bases.