Frames and bases in tensor products of Hilbert spaces and Hilbert C*-modules |
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| Authors: | Amir Khosravi Behrooz Khosravi |
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| Affiliation: | (1) Faculty of Mathematical Sciences and Computer Engineering, University for Teacher Education, 599 Taleghani Ave., Tehran, 15614, Iran;(2) Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran, 15914, Iran |
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| Abstract: | ![]()
In this article, we study tensor product of Hilbert C*-modules and Hilbert spaces. We show that if E is a Hilbert A-module and F is a Hilbert B-module, then tensor product of frames (orthonormal bases) for E and F produce frames (orthonormal bases) for Hilbert A ⊗ B-module E ⊗ F, and we get more results. For Hilbert spaces H and K, we study tensor product of frames of subspaces for H and K, tensor product of resolutions of the identities of H and K, and tensor product of frame representations for H and K. |
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| Keywords: | Frame frame operator tensor product Hilbert C*-module |
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