Frames and Bases in Tensor Products of Hilbert Spaces and Hilbert 𝐶*-Modules

Proceedings Mathematical Sciences

Amir Khosravi¹  Behrooz Khosravi² 

[1] Faculty of Mathematical Sciences and Computer Engineering, University for Teacher Education, Taleghani Ave., Tehran , Iran$$;Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), , Hafez Ave., Tehran , Iran$$

关键词: Frame;    frame operator;    tensor product;    Hilbert 𝐶*-module.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown