• Frames and Bases in Tensor Products of Hilbert Spaces and Hilbert $C^\ast$-Modules

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/117/01/0001-0012

• # Keywords

Frame; frame operator; tensor product; Hilbert $C^∗$-module.

• # 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 $A \otimes B$-module $E \otimes F$, 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.

• # Author Affiliations

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 4
September 2019