Multipliers for von Neumann-Schatten Bessel sequences in separable Banach spaces

TL;DR

This paper introduces von Neumann-Schatten Bessel multipliers in Banach spaces, characterizes their properties, and explores invertible Hilbert-Schmidt frame multipliers, with implications for matrix diagonalization and dual g-frames.

Contribution

It presents the concept of von Neumann-Schatten Bessel multipliers and analyzes their properties, including invertibility, in the context of Banach and Hilbert spaces.

Findings

Characterization of von Neumann-Schatten Bessel multipliers

Analysis of invertible Hilbert-Schmidt frame multipliers

Implications for matrix diagonalization and dual g-frames

Abstract

In this paper we introduce the concept of von Neumann-Schatten Bessel multipliers and obtain some of their characterizations. Finally, special attention is devoted to the study of invertible Hilbert--Schmidt frame multipliers. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for diagonalization of matrices in finite dimensional setting as well as for dual $g$-frames. In particular, we show that a $g$-frame is uniquely determined by the set of its $g$-frames.