Generalized atomic subspaces for operators in Hilbert spaces

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.

22 pages

Cited by in corpus (6)

• Continuous controlled generalized fusion frames in Hilbert spaces
• Generalized fusion frame in tensor product of Hilbert spaces
• Atomic systems in n-Hilbert spaces and their tensor products
• Construction of continuous controlled K-g-fusion frames in Hilbert spaces
• Weaving continuous controlled K-g-fusion frames in Hilbert spaces
• Controlled g-atomic subspaces for operators in Hilbert spaces