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Continuous frames in n-Hilbert spaces and their tensor products

Prasenjit Ghosh, T. K. Samanta

TL;DR

The concept of continuous frame for the tensor products of n-Hilbert spaces is introduced which is a generalization of discrete frame in n-hilbert space and dual continuous frame and continuous Bessel multiplier are studied.

Abstract

We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept of continuous frame for the tensor products of n-Hilbert spaces. Further, we study dual continuous frame and continuous Bessel multiplier in n-Hilbert spaces and their tensor products.

Continuous frames in n-Hilbert spaces and their tensor products

TL;DR

The concept of continuous frame for the tensor products of n-Hilbert spaces is introduced which is a generalization of discrete frame in n-hilbert space and dual continuous frame and continuous Bessel multiplier are studied.

Abstract

We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept of continuous frame for the tensor products of n-Hilbert spaces. Further, we study dual continuous frame and continuous Bessel multiplier in n-Hilbert spaces and their tensor products.
Paper Structure (4 sections, 73 equations)

This paper contains 4 sections, 73 equations.

Table of Contents

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

Theorems & Definitions (10)

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