Generalized atomic subspaces for operators in Hilbert spaces

TL;DR

This paper introduces generalized atomic subspaces for operators in Hilbert spaces, utilizing g-fusion frames to develop resolutions of the identity and analyze frame operators.

Contribution

It proposes a new concept of g-atomic subspaces and explores their properties within the framework of g-fusion frames in Hilbert spaces.

Findings

Development of g-atomic subspaces for bounded linear operators

Construction of resolutions of the identity operator using g-fusion frames

Analysis of frame operators for g-fusion Bessel sequences

Abstract

We introduce the notion of a g-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of g-fusion frames. Also we shall describe the concept of frame operator for a pair of g-fusion Bessel sequences and some of their properties.