Some New Notions of Bases for the Range of Operators in Hilbert Spaces
This paper is devoted to introduce a new concept of bases for the range of the operator $K$. Actually, we consider controlled $K$-orthonormal and controlled $K$-Riesz bases which are a generalization of ordinary bases in Hilbert spaces. In the sequel, we give some characterizations of these sequenc...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2024-07-01
|
| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_712163_3bc35bd78ca25bdad6be1e257ba1046c.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823859419286339584 |
|---|---|
| author | Hessam Hosseinnezhad |
| author_facet | Hessam Hosseinnezhad |
| author_sort | Hessam Hosseinnezhad |
| collection | DOAJ |
| description | This paper is devoted to introduce a new concept of bases for the range of the operator $K$. Actually, we consider controlled $K$-orthonormal and controlled $K$-Riesz bases which are a generalization of ordinary bases in Hilbert spaces. In the sequel, we give some characterizations of these sequences. Next, we construct some new controlled bases with operator theory tools. Finally, some dual characterizations are given. |
| format | Article |
| id | doaj-art-aaa6bcf797714f3d925b08c5dc5441f9 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-aaa6bcf797714f3d925b08c5dc5441f92025-02-11T05:27:31ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-07-0121324926610.22130/scma.2023.2009830.1435712163Some New Notions of Bases for the Range of Operators in Hilbert SpacesHessam Hosseinnezhad0Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran.This paper is devoted to introduce a new concept of bases for the range of the operator $K$. Actually, we consider controlled $K$-orthonormal and controlled $K$-Riesz bases which are a generalization of ordinary bases in Hilbert spaces. In the sequel, we give some characterizations of these sequences. Next, we construct some new controlled bases with operator theory tools. Finally, some dual characterizations are given.https://scma.maragheh.ac.ir/article_712163_3bc35bd78ca25bdad6be1e257ba1046c.pdfcontrolled framek-frameriesz basisorthonormal basis |
| spellingShingle | Hessam Hosseinnezhad Some New Notions of Bases for the Range of Operators in Hilbert Spaces Sahand Communications in Mathematical Analysis controlled frame k-frame riesz basis orthonormal basis |
| title | Some New Notions of Bases for the Range of Operators in Hilbert Spaces |
| title_full | Some New Notions of Bases for the Range of Operators in Hilbert Spaces |
| title_fullStr | Some New Notions of Bases for the Range of Operators in Hilbert Spaces |
| title_full_unstemmed | Some New Notions of Bases for the Range of Operators in Hilbert Spaces |
| title_short | Some New Notions of Bases for the Range of Operators in Hilbert Spaces |
| title_sort | some new notions of bases for the range of operators in hilbert spaces |
| topic | controlled frame k-frame riesz basis orthonormal basis |
| url | https://scma.maragheh.ac.ir/article_712163_3bc35bd78ca25bdad6be1e257ba1046c.pdf |
| work_keys_str_mv | AT hessamhosseinnezhad somenewnotionsofbasesfortherangeofoperatorsinhilbertspaces |