@article {
author = {Hasankhani Fard, Mohammad Ali},
title = {Simple Construction of a Frame which is $\epsilon$-nearly Parseval and $\epsilon$-nearly Unit Norm},
journal = {Sahand Communications in Mathematical Analysis},
volume = {16},
number = {1},
pages = {57-67},
year = {2019},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.79613.374},
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 $\left\{f_k\right\}_{k=1}^\infty$ and $\left\{Tf_k\right\}_{k=1}^\infty$ are $\epsilon$-nearly equal frame operators, where $\left\{f_k\right\}_{k=1}^\infty$ is a frame for $\mathcal{H}$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.},
keywords = {Frame,Parseval frame,$epsilon$-nearly Parseval frame,$epsilon$-nearly equal frame operators,Operator dual Parseval frames},
url = {https://scma.maragheh.ac.ir/article_36056.html},
eprint = {https://scma.maragheh.ac.ir/article_36056_f35fed1254b0f7e914d2501ed969db8f.pdf}
}