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$K$-orthonormal and $K$-Riesz Bases

Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 1)

Publication Date:

Authors : ; ;

Page : 59-72

Keywords : $K$-frame; Riesz basis; Orthonormal basis; Atomic system;

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Abstract

Let $K$ be a bounded operator. $K$-frames are ordinary frames for the range $K$. These frames are a generalization of ordinary frames and are certainly different from these frames. This research introduces a new concept of bases for the range $K$. Here we define the  $K$-orthonormal basis and the $K$-Riesz basis, and then we describe their properties. As might be expected, the $K$-bases differ from the ordinary ones mentioned in this article.

Last modified: 2021-11-03 14:31:28