Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm
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 fra...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2019-10-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_36056_f35fed1254b0f7e914d2501ed969db8f.pdf |
| _version_ | 1818290639190622208 |
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| author | Mohammad Ali Hasankhani Fard |
| author_facet | Mohammad Ali Hasankhani Fard |
| author_sort | Mohammad Ali Hasankhani Fard |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T02:31:22Z |
| format | Article |
| id | doaj.art-7ca3cd58741946ce83e558e844fde3d8 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-12-13T02:31:22Z |
| publishDate | 2019-10-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-7ca3cd58741946ce83e558e844fde3d82022-12-22T00:02:30ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002019-10-01161576710.22130/scma.2018.79613.37436056Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit NormMohammad Ali Hasankhani Fard0Department of Mathematics Vali-e-Asr University, Rafsanjan, Iran.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.http://scma.maragheh.ac.ir/article_36056_f35fed1254b0f7e914d2501ed969db8f.pdfFrameParseval frame$epsilon$-nearly Parseval frame$epsilon$-nearly equal frame operatorsOperator dual Parseval frames |
| spellingShingle | Mohammad Ali Hasankhani Fard Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm Sahand Communications in Mathematical Analysis Frame Parseval frame $epsilon$-nearly Parseval frame $epsilon$-nearly equal frame operators Operator dual Parseval frames |
| title | Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm |
| title_full | Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm |
| title_fullStr | Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm |
| title_full_unstemmed | Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm |
| title_short | Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm |
| title_sort | simple construction of a frame which is epsilon nearly parseval and epsilon nearly unit norm |
| topic | Frame Parseval frame $epsilon$-nearly Parseval frame $epsilon$-nearly equal frame operators Operator dual Parseval frames |
| url | http://scma.maragheh.ac.ir/article_36056_f35fed1254b0f7e914d2501ed969db8f.pdf |
| work_keys_str_mv | AT mohammadalihasankhanifard simpleconstructionofaframewhichisepsilonnearlyparsevalandepsilonnearlyunitnorm |