Khurana, D and Roy, S and Sain, D (2020) Symmetric points in spaces of linear operators between banach spaces. In: Acta Scientiarum Mathematicarum, 86 (3-4). pp. 617-634.
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We explore the relation between left-symmetry (right-symmetry) of elements in a real Banach space and right-symmetry (left-symmetry) of their supporting functionals. We obtain a complete characterization of symmetric functionals on a reflexive, strictly convex and smooth Banach space. We also prove that a bounded linear operator from a reflexive, Kadets-Klee and strictly convex Banach space to any Banach space is symmetric if and only if it is the zero operator. We further characterize left-symmetric operators from ℓn1, n ≥ 2, to any Banach space X. This improves a previously obtained characterization of left-symmetric operators from ℓn1, n ≥ 2, to a reflexive smooth Banach space X.
| Item Type: | Journal Article |
|---|---|
| Publication: | Acta Scientiarum Mathematicarum |
| Publisher: | University of Szeged |
| Additional Information: | The copyright for this article belongs to University of Szeged. |
| Keywords: | Birkhoff-James orthogonality; Left-symmetric point; Right-symmetric point; Supporting functional; Symmetric operator |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 07 Feb 2023 10:40 |
| Last Modified: | 07 Feb 2023 10:40 |
| URI: | https://eprints.iisc.ac.in/id/eprint/80008 |
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