Some generalizations of frames in Hilbert modules

TL;DR

This paper introduces generalized frames for endomorphisms in Hilbert modules, expanding the theoretical framework and providing new results that could impact various scientific and engineering applications.

Contribution

It presents novel concepts of frames for endomorphisms in Hilbert modules and derives new theoretical results for these generalized frames.

Findings

Introduction of frames for $End_{ ext{A}}^{ ext{*}}( ext{H, K})$

New results on generalized frames in Hilbert modules

Potential applications in science and engineering

Abstract

Frames play significant role in various areas of science and engineering. In this paper, we introduce the concepts of frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H, K})$ and their generalizations. Moreover, we obtain some new results for generalized frames in Hilbert modules.