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

摘要

In this article, we study tensor product of Hilbert e???*-modules and Hilbert spaces. We show that if e??? is a Hilbert e??′-module and e??1 is a Hilbert e??μ-module, then tensor product of frames (orthonormal bases) for e??? and e??1 produce frames (orthonormal bases) for Hilbert $A otimes B$-module $E otimes F$, and we get more results.For Hilbert spaces e??? and e???, we study tensor product of frames of subspaces for e??? and e???, tensor product of resolutions of the identities of e??? and e???, and tensor product of frame representations for e??? and e???.