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Continuous K-biframes in Hilbert spaces and their tensor products

Prasenjit Ghosh, T. K. Samanta

Abstract

A generalization of continuous biframe in a Hilbert space is introduced and a few examples are discussed. Some characterizations and algebraic properties of this biframe are given. Here we also construct various types of continuous K-biframes with the help of a bounded linear operator. Relationship between continuous K-biframe and quotient operator is established. Finally, we define continuous K-biframe for the tensor products of Hilbert spaces and give an example.

Continuous K-biframes in Hilbert spaces and their tensor products

Abstract

A generalization of continuous biframe in a Hilbert space is introduced and a few examples are discussed. Some characterizations and algebraic properties of this biframe are given. Here we also construct various types of continuous K-biframes with the help of a bounded linear operator. Relationship between continuous K-biframe and quotient operator is established. Finally, we define continuous K-biframe for the tensor products of Hilbert spaces and give an example.
Paper Structure (5 sections, 102 equations)

This paper contains 5 sections, 102 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Continuous $K$-biframe in Hilbert space
  4. Continuous $K$-biframes and operators
  5. Continuous $K_{1} \,\otimes\, K_{2}$-biframe in $H_{1} \,\otimes\, H_{2}$

Theorems & Definitions (17)

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  • ...and 7 more