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Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm

Journal: Sahand Communications in Mathematical Analysis (Vol.16, No. 1)

Publication Date:

Authors : ;

Page : 57-67

Keywords : Frame; Parseval frame; $epsilon$-nearly Parseval frame; $epsilon$-nearly equal frame operators; Operator dual Parseval frames;

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Abstract

In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible operators $T$ on the finite or infinite dimensional Hilbert space $mathcal{H}$ such that $left{f_kright}_{k=1}^infty$ and $left{Tf_kright}_{k=1}^infty$ are $epsilon$-nearly equal frame operators, where $left{f_kright}_{k=1}^infty$ is a frame for $mathcal{H}$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.

Last modified: 2019-10-14 16:37:35