Atomic systems in n-Hilbert spaces and their tensor products

TL;DR

This paper explores atomic systems and K-frames within n-Hilbert spaces and their tensor products, providing new characterizations and relationships to advance understanding of their structure and applications.

Contribution

It introduces a novel framework for atomic systems and K-frames in tensor products of n-Hilbert spaces, with new characterizations and relationships.

Findings

Characterization of K-frames in tensor products of n-Hilbert spaces

Establishment of relationships between atomic systems in n-Hilbert spaces and their tensor products

Development of a framework for local atoms in n-Hilbert spaces

Abstract

Concept of a family of local atoms in n-Hilbert space is being studied. K-frame in tensor product of n-Hilbert spaces is described and a characterization is given. Atomic system in tensor product of n-Hilbert spaces is presented and established a relationship between atomic systems in n-Hilbert spaces and their tensor products.