Controlled frames in n-Hilbert spaces and their tensor products

TL;DR

This paper introduces controlled frames in n-Hilbert spaces, explores their properties, duals, and tensor products, and examines their relationship with bounded operators and direct sums, expanding the theoretical framework of frame theory.

Contribution

It extends the concept of controlled frames to n-Hilbert spaces, providing new characterizations and analyzing their tensor products and operator relationships.

Findings

Characterization of controlled frames in n-Hilbert spaces

Relationship between controlled frames and bounded linear operators in tensor products

Analysis of direct sums of controlled frames

Abstract

The concepts of controlled frames and it's dual in n-Hilbert spaces and their tensor products have been introduced and then some of their characterizations are given. We further study the relationship between controlled frame and bounded linear operator in tensor product of n-Hilbert spaces. At the end, the direct sum of controlled frames in n-Hilbert space is being considered.