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 130, 2020
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