Birkhoff-James orthogonality and applications : A survey
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910362776895488 |
|---|---|
| author | Grover, Priyanka Singla, Sushil |
| author_facet | Grover, Priyanka Singla, Sushil |
| contents | In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain Banach spaces are mentioned. Their applications in studying the geometry of normed spaces are given. The connections between this concept of orthogonality, and the Gateaux derivative and the subdifferential set of the norm function are provided. Several interesting distance formulas can be obtained using the characterizations of Birkhoff-James orthogonality, which are also mentioned. In the end, some new results are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_07399 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Birkhoff-James orthogonality and applications : A survey Grover, Priyanka Singla, Sushil Functional Analysis 15A60, 41A50, 46B20, 46L05, 46L08, 46G05, 47B47 In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain Banach spaces are mentioned. Their applications in studying the geometry of normed spaces are given. The connections between this concept of orthogonality, and the Gateaux derivative and the subdifferential set of the norm function are provided. Several interesting distance formulas can be obtained using the characterizations of Birkhoff-James orthogonality, which are also mentioned. In the end, some new results are obtained. |
| title | Birkhoff-James orthogonality and applications : A survey |
| topic | Functional Analysis 15A60, 41A50, 46B20, 46L05, 46L08, 46G05, 47B47 |
| url | https://arxiv.org/abs/2005.07399 |