Articles written in Proceedings – Mathematical Sciences
Volume 117 Issue 1 February 2007 pp 1-12
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.
Volume 121 Issue 2 May 2011 pp 155-164
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.