Introduction of Frame in Tensor Product of $n$-Hilbert Spaces

Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 4)

Publication Date: 2021-12-05

Authors : Prasenjit Ghosh; Tapas Kumar Samanta;

Page : 1-18

Keywords : Frame; Dual frame; Tensor product of Hilbert spaces; $n$-normed space; $n$-Hilbert space;

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Abstract

We study the concept of frame in tensor product of $n$-Hilbert spaces as tensor product of $n$-Hilbert spaces is again an $n$-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship between frame and bounded linear operator in tensor product of $n$-Hilbert spaces is studied. Finally,;the dual frame in tensor product of $n$-Hilbert spaces is discussed.

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Introduction of Frame in Tensor Product of $n$-Hilbert Spaces

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