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

2007/03/20 by Amir Khosravi, Khosravi, Amir, Behrooz Khosravi +1
Earth and Planetary Sciences · Mathematics · Medicine · #42C15 #46H25 #46L99 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Operator Algebras (math.OA) #Seismic Imaging and Inversion Techniques #math.OA #msc:42C15 #msc:46H25 #msc:46L99

paper · pdf · doi:10.48550/arxiv.math/0703582

12 pages

arxiv created 2007/03/20 · openalex publication_date 2007/03/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Continuous and Discrete Wavelet Transforms

Related

• *-K-g-Frames and their duals for Hilbert A-modules
• Extension of frames and bases - I
• Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations
• A-2-Frames in A-2-inner product spaces
• K-frames in Hilbert C^*-modules