Symmetric points in spaces of linear operators between Banach spaces
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...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2020
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| Sorozat: | Acta scientiarum mathematicarum
86 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-020-420-6 |
| Online Access: | http://acta.bibl.u-szeged.hu/73907 |
| Tartalmi kivonat: | 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 ℓ n 1 , n ≥ 2, to any Banach space X. This improves a previously obtained characterization of left-symmetric operators from ℓ n 1 , n ≥ 2, to a reflexive smooth Banach space X. |
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| Terjedelem/Fizikai jellemzők: | 617-634 |
| ISSN: | 2064-8316 |