Controlled g-atomic subspaces for operators in Hilbert spaces

TL;DR

This paper introduces controlled g-atomic subspaces for bounded linear operators in Hilbert spaces, providing characterizations, examples, and constructions of controlled K-g-fusion frames with applications to resolutions of the identity operator.

Contribution

It presents a new framework for controlled g-atomic subspaces and controlled K-g-fusion frames, including their construction and properties in Hilbert spaces.

Findings

Provided a characterization of controlled g-atomic subspaces.

Constructed a new controlled K-g-fusion frame for Hilbert spaces.

Discussed resolutions of the identity operator using controlled g-fusion frames.

Abstract

Controlled g-atomic subspace for a bounded linear operator is being presented and a characterization has been given. We give an example of controlled K-g-fusion frame. We construct a new controlled K-g-fusion frame for the Hilbert space H ? X using the controlled K-g-fusion frames of the Hilbert spaces H and X. Several useful resolutions of the identity operator on a Hilbert space using the theory of controlled g-fusion frames have been discussed. Frame operator for a pair of controlled g-fusion Bessel sequences has been introduced.