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Generalized atomic subspaces for operators in Hilbert spaces

Prasenjit Ghosh, T. K. Samanta

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.

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.

Paper Structure

This paper contains 5 sections, 175 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Resolution of the identity operator in $g$-fusion frame
  4. $g$-atomic subspace
  5. Frame operator for a pair of $g$-fusion Bessel sequences

Theorems & Definitions (16)

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  • ...and 6 more