Controlled g-atomic subspaces for operators in Hilbert spaces

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.

21 pages. arXiv admin note: text overlap with arXiv:2102.01965

References in corpus (3)

• Generalized atomic subspaces for operators in Hilbert spaces
• Stability of dual g-fusion frames in Hilbert spaces
• Generalized fusion frame in tensor product of Hilbert spaces