Adjoint of sums and products of operators in Hilbert spaces
We provide sufficient and necessary conditions guaranteeing equations (A + B)* = A* + B* and (AB)* = B*A* concerning densely defined unbounded operators A, B between Hilbert spaces. We also improve the perturbation theory of selfadjoint and essentially selfadjoint operators due to Nelson, Kato, Rell...
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| Dokumentumtípus: | Cikk |
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Bolyai Institute, University of Szeged
Szeged
2016
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| Sorozat: | Acta scientiarum mathematicarum
82 No. 1-2 |
| Kulcsszavak: | Operátorok, Hilbert-tér, Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/40284 |
| Tartalmi kivonat: | We provide sufficient and necessary conditions guaranteeing equations (A + B)* = A* + B* and (AB)* = B*A* concerning densely defined unbounded operators A, B between Hilbert spaces. We also improve the perturbation theory of selfadjoint and essentially selfadjoint operators due to Nelson, Kato, Rellich, and Wiist. Our method involves the range of two-by-two matrices of the form MS,T = ( ) that makes it possible to treat real and complex Hilbert spaces jointly. |
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| Terjedelem/Fizikai jellemzők: | 175-191 |
| ISSN: | 0001-6969 |