A Study of Birkhoff Orthogonal Sets in Smooth Banach Spaces
Referring to the definition of orthogonal set in inner product space，the concept of Birkhoff orthogonal set is introduced in finite-dimensional real Banach spaces，and the problem of whether there exists a Birkhoff orthogonal set whose number of elements exceeds the space dimension is studied in s...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | Chinese |
| Published: |
Harbin University of Science and Technology Publications
2024-02-01
|
| Series: | Journal of Harbin University of Science and Technology |
| Subjects: | |
| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2304 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1839630150482788352 |
|---|---|
| author | WANG Xiaomei JI Donghai |
| author_facet | WANG Xiaomei JI Donghai |
| author_sort | WANG Xiaomei |
| collection | DOAJ |
| description |
Referring to the definition of orthogonal set in inner product space，the concept of Birkhoff orthogonal set is introduced in finite-dimensional real Banach spaces，and the problem of whether there exists a Birkhoff orthogonal set whose number of elements exceeds the space dimension is studied in smooth Banach spaces．It is proved that there is no Birkhoff orthogonal set whose number of elements exceeds the space dimension in two-dimensional smooth Banach spaces． In a smooth Banach space with more than three dimensions，there is no Birkhoff orthogonal set with more elements than the space dimension and all the elements are left ( right) symmetric points．It is also proved that if there is a Birkhoff orthogonal set A = { x1 ，x2 ，… , xn，xn + 1 } in an n-dimensional ( n ≥3)smooth Banach space，and then A must not satisfy the following two conditions: ( 1) for each xm ∈A，there exists xm 丄B xi ( Yi≠m) ; ( 2) for each xm ∈A，there exists xi 丄B xm ( Yi≠m) . |
| format | Article |
| id | doaj-art-92bd0a7bf77a4913af6dce94ece7366b |
| institution | Matheson Library |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2024-02-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-92bd0a7bf77a4913af6dce94ece7366b2025-07-14T10:11:15ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832024-02-01290114314910.15938/j.jhust.2024.01.016A Study of Birkhoff Orthogonal Sets in Smooth Banach SpacesWANG Xiaomei0JI Donghai1College of Science，Harbin University of Science and Technology，Harbin 150080，ChinaCollege of Science，Harbin University of Science and Technology，Harbin 150080，China Referring to the definition of orthogonal set in inner product space，the concept of Birkhoff orthogonal set is introduced in finite-dimensional real Banach spaces，and the problem of whether there exists a Birkhoff orthogonal set whose number of elements exceeds the space dimension is studied in smooth Banach spaces．It is proved that there is no Birkhoff orthogonal set whose number of elements exceeds the space dimension in two-dimensional smooth Banach spaces． In a smooth Banach space with more than three dimensions，there is no Birkhoff orthogonal set with more elements than the space dimension and all the elements are left ( right) symmetric points．It is also proved that if there is a Birkhoff orthogonal set A = { x1 ，x2 ，… , xn，xn + 1 } in an n-dimensional ( n ≥3)smooth Banach space，and then A must not satisfy the following two conditions: ( 1) for each xm ∈A，there exists xm 丄B xi ( Yi≠m) ; ( 2) for each xm ∈A，there exists xi 丄B xm ( Yi≠m) .https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2304banach spacebirkhoff orthogonalitybirkhoff orthogonal setsmoothness |
| spellingShingle | WANG Xiaomei JI Donghai A Study of Birkhoff Orthogonal Sets in Smooth Banach Spaces Journal of Harbin University of Science and Technology banach space birkhoff orthogonality birkhoff orthogonal set smoothness |
| title | A Study of Birkhoff Orthogonal Sets in Smooth Banach Spaces |
| title_full | A Study of Birkhoff Orthogonal Sets in Smooth Banach Spaces |
| title_fullStr | A Study of Birkhoff Orthogonal Sets in Smooth Banach Spaces |
| title_full_unstemmed | A Study of Birkhoff Orthogonal Sets in Smooth Banach Spaces |
| title_short | A Study of Birkhoff Orthogonal Sets in Smooth Banach Spaces |
| title_sort | study of birkhoff orthogonal sets in smooth banach spaces |
| topic | banach space birkhoff orthogonality birkhoff orthogonal set smoothness |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2304 |
| work_keys_str_mv | AT wangxiaomei astudyofbirkhofforthogonalsetsinsmoothbanachspaces AT jidonghai astudyofbirkhofforthogonalsetsinsmoothbanachspaces AT wangxiaomei studyofbirkhofforthogonalsetsinsmoothbanachspaces AT jidonghai studyofbirkhofforthogonalsetsinsmoothbanachspaces |