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.

Atomic systems in n-Hilbert spaces and their tensor products

“…K-frames for a separable Hilbert spaces were introduced by Lara Gavruta [4] to study atomic decomposition systems for a bounded linear operator. Infact, generalized atomic subspaces for operators in Hilbert spaces were studied by P. Ghosh and T. K. Samanta [7]. Kframe is also presented to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space and it is a generalization of the ordinary frames.…”

Some properties of K-frame in n-Hilbert space

“…K-frames are more generalization than the ordinary frames and many properties of ordinary frames may not holds for such generalization of frames. Generalized atomic subspaces for operators in Hilbert spaces were studied by P. Ghosh and T. K. Samanta [8] and they were also presented the stability of dual g-fusion frames in Hilbert spaces in [7].…”