Introduction of frame in tensor product of n-Hilbert spaces

TL;DR

This paper explores the concept of frames within tensor products of n-Hilbert spaces, generalizing known basis results, examining relationships with bounded operators, and discussing dual frames in this context.

Contribution

It introduces the notion of frames in tensor products of n-Hilbert spaces, extending basis results and analyzing their relation to bounded operators and dual frames.

Findings

Frames in tensor products of n-Hilbert spaces are well-defined.

Generalization of basis results to frames in this setting.

Relationship established between frames and bounded linear operators.

Abstract

We study the concept of frame in tensor product of n-Hilbert spaces as tensor product of n-Hilbert spaces is again a n-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship between frame and bounded linear operator in tensor product of n-Hilbert spaces is studied. Finally, the dual frame in tensor product of n-Hilbert spaces is discussed.