E-frames multipliers

Abstract

$E$-frames are a new generalization for the concept of frames for $\mathcal{H}$, where $E$ is an infinite invertible complex matrix mapping on ${⨁}_{n=1}^{\infty }\mathcal{H}$. This article is dedicated to investigating some notions related to $E$-Bessel sequences and $E$-multipliers. A Multiplier is an operator created by frame-like analysis, multiplication with a fixed sequence, called the symbol, and synthesis. In this article, we introduce the notion of $E$-multipliers, which generalizes multipliers for $E$-sequences and study their properties, including boundedness and invertibility.