Continuous frames in n-Hilbert spaces and their tensor products

TL;DR

This paper introduces continuous frames in n-Hilbert spaces, extends the concept to tensor products, and explores dual frames and Bessel multipliers, broadening the mathematical framework for these structures.

Contribution

It generalizes discrete frames to continuous frames in n-Hilbert spaces and develops their tensor product counterparts, including duals and multipliers.

Findings

Defined continuous frames in n-Hilbert spaces

Established continuous frames for tensor products of n-Hilbert spaces

Analyzed dual frames and Bessel multipliers in this context

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.