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Introduction of frame in tensor product of n-Hilbert spaces

Prasenjit Ghosh, Tapas Kumar Samanta

Abstract

We study the concept of frame in tensor product of n-Hilbert spaces as tensor product of n-Hilbert spaces is again a n-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship between frame and bounded linear operator in tensor product of n-Hilbert spaces is studied. Finally, the dual frame in tensor product of n-Hilbert spaces is discussed.

Introduction of frame in tensor product of n-Hilbert spaces

Abstract

We study the concept of frame in tensor product of n-Hilbert spaces as tensor product of n-Hilbert spaces is again a n-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship between frame and bounded linear operator in tensor product of n-Hilbert spaces is studied. Finally, the dual frame in tensor product of n-Hilbert spaces is discussed.

Paper Structure

This paper contains 4 sections, 13 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Frame in tensor product of $n$-Hilbert spaces
  4. Dual frame in tensor product of $n$-Hilbert spaces

Key Result

Theorem 2.5

Folland Suppose $Q,\, Q^{\prime} \,\in\, \mathcal{B}\,(\,X\,)$ and $T,\, T^{\prime} \,\in\, \mathcal{B}\,(\,Y\,)$. Then

Theorems & Definitions (40)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Theorem 2.5
  • Definition 2.6
  • Definition 2.7
  • Theorem 2.8
  • Theorem 2.9
  • Definition 2.10
  • ...and 30 more