Sen, J and Sain, D and Paul, K (2021) On approximate orthogonality and symmetry of operators in semi-Hilbertian structure. In: Bulletin des Sciences Mathematiques, 170 .
|
PDF
bul_des_sci_170_2021.pdf - Published Version Download (439kB) | Preview |
Abstract
The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator A on a Hilbert space H, we define (ϵ,A)-approximate orthogonality and (ϵ,A)-approximate orthogonality in the sense of Chmieliński and establish a relation between them. We also characterize (ϵ,A)-approximate orthogonality in the sense of Chmieliński for A-bounded and A-bounded compact operators. We further generalize the concept of right symmetric and left symmetric operators on a Hilbert space. The utility of these notions is illustrated by extending some of the previous results obtained by various authors in the setting of Hilbert spaces.
| Item Type: | Journal Article |
|---|---|
| Publication: | Bulletin des Sciences Mathematiques |
| Publisher: | Elsevier Masson s.r.l. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Approximate orthogonality; Compact operators; Left symmetric point; Norm attainment set; Positive operators; Right symmetric point |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 15 May 2023 10:03 |
| Last Modified: | 15 May 2023 10:03 |
| URI: | https://eprints.iisc.ac.in/id/eprint/81650 |
Actions (login required)
 |
View Item |
