On a subclass of norm attaining operators
A bounded linear operator T : H1 → H2, where H1, H2 are Hilbert spaces, is said to be norm attaining if there exists a unit vector x ∈ H1 such that kT xk = kTk and absolutely norm attaining (or AN -operator) if T|M : M → H2 is norm attaining for every closed subspace M of H1. We prove a structure th...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
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| Sorozat: | Acta scientiarum mathematicarum
87 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-020-426-9 |
| Online Access: | http://acta.bibl.u-szeged.hu/73928 |
| Tartalmi kivonat: | A bounded linear operator T : H1 → H2, where H1, H2 are Hilbert spaces, is said to be norm attaining if there exists a unit vector x ∈ H1 such that kT xk = kTk and absolutely norm attaining (or AN -operator) if T|M : M → H2 is norm attaining for every closed subspace M of H1. We prove a structure theorem for positive operators in β(H) := {T ∈ B(H) : T|M : M → M is norm attaining for all M ∈ RT }, where RT is the set of all reducing subspaces of T. We also compare our results with those of absolutely norm attaining operators. Later, we characterize all operators in this new class. |
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| Terjedelem/Fizikai jellemzők: | 247-263 |
| ISSN: | 2064-8316 |