• Behrooz Khosravi

Articles written in Proceedings – Mathematical Sciences

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

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.

• Fusion Frames and 𝐺-Frames in Banach Spaces

Fusion frames and 𝑔-frames in Hilbert spaces are generalizations of frames, and frames were extended to Banach spaces. In this article we introduce fusion frames, 𝑔-frames, Banach 𝑔-frames in Banach spaces and we show that they share many useful properties with their corresponding notions in Hilbert spaces. We also show that 𝑔-frames, fusion frames and Banach 𝑔-frames are stable under small perturbations and invertible operators.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019