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Proceedings Mathematical Sciences

, Volume 117, Issue 1, pp 1–12 | Cite as

Frames and bases in tensor products of Hilbert spaces and Hilbert C*-modules

  • Amir Khosravi
  • Behrooz Khosravi
Open Access
Article

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 AB-module EF, 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.

Keywords

Frame frame operator tensor product Hilbert C*-module 

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Copyright information

© Indian Academy of Sciences 2007

Authors and Affiliations

  • Amir Khosravi
    • 1
  • Behrooz Khosravi
    • 2
  1. 1.Faculty of Mathematical Sciences and Computer EngineeringUniversity for Teacher EducationTehranIran
  2. 2.Department of Pure Mathematics, Faculty of Mathematics and Computer ScienceAmirkabir University of Technology (Tehran Polytechnic)TehranIran

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