Solvability of The Operator Equations $ AX-XB=C $ and $ AX-YB=C $
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908614380224512 |
|---|---|
| author | Lombarkia, Farida Bezai, Assia Thome, Néstor |
| author_facet | Lombarkia, Farida Bezai, Assia Thome, Néstor |
| contents | This paper provides new necessary and sufficient conditions for the solvability to the operator equations $ AX-XB=C$ and $AX-YB=C,$ where $A $ and $B $ are group invertible operators defined on an infinite dimensional Hilbert space. In addition, the general solutions to the equation $AX-YB=C,$ are derived in terms of group inverse of $ A $ and $ B $. As a consequence, new necessary and sufficient conditions for the solvability to the operator equation $ AYB-Y=C,$ are derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solvability of The Operator Equations $ AX-XB=C $ and $ AX-YB=C $ Lombarkia, Farida Bezai, Assia Thome, Néstor Functional Analysis 47A62, 15A09 This paper provides new necessary and sufficient conditions for the solvability to the operator equations $ AX-XB=C$ and $AX-YB=C,$ where $A $ and $B $ are group invertible operators defined on an infinite dimensional Hilbert space. In addition, the general solutions to the equation $AX-YB=C,$ are derived in terms of group inverse of $ A $ and $ B $. As a consequence, new necessary and sufficient conditions for the solvability to the operator equation $ AYB-Y=C,$ are derived. |
| title | Solvability of The Operator Equations $ AX-XB=C $ and $ AX-YB=C $ |
| topic | Functional Analysis 47A62, 15A09 |
| url | https://arxiv.org/abs/2510.23132 |