Frames and Bases in Tensor Product of Hilbert Spaces
Functional Analysis
2012-04-03 v1
Abstract
In this article we develop a theory for frames in tensor product of Hilbert spaces. We show that like bases if Y_1, Y_2, \cdot \cdot \cdot, Y_n are frames for H_1,H_2, \cdot \cdot \cdot, H_n, respectively, then Y_1\otimesY_2\otimes...\otimesY_n is a frame for H_\otimes1H_2\otimes \cdot \cdot \cdot \otimesH_n. Moreover we consider the canonical dual frame in tensor product space. We further obtain a relation between the dual frames in Hilbert spaces, and their tensor product.
Cite
@article{arxiv.1204.0096,
title = {Frames and Bases in Tensor Product of Hilbert Spaces},
author = {Amir Khosravi and Mohammad Sadegh Asgari},
journal= {arXiv preprint arXiv:1204.0096},
year = {2012}
}
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12 pages