Frames and Bases in Tensor Product of Hilbert Spaces

Details Frames and Bases in Tensor Product of Hilbert Spaces Frames and Bases in Tensor Product of Hilbert Spaces

2012-03-31

arxiv.org/abs/1204.0096v1

Intern. Math. Journal, Vol. 4, 2003, no. 6, 527 - 537

Mathematics

Functional Analysis

12 pages

Scientific paper

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.

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