Extreme points of numerical ranges of quasihyponormal operators
It is shown that a quasihypnormal operator on a Hilbert space having 0 as a boundary point of its numerical range is hyponormal. A necessary and sufficient condition is given for the extreme points of the numerical range of a quasihyponormal operator to be eigenvalues. It is also established that if...
- Autores:
-
Rodríguez Montes, Jaime
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1993
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43617
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43617
http://bdigital.unal.edu.co/33715/
- Palabra clave:
- Operator quasihypnormal
Hilbert space
breakpoint
numerical range is hyponormal
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | It is shown that a quasihypnormal operator on a Hilbert space having 0 as a boundary point of its numerical range is hyponormal. A necessary and sufficient condition is given for the extreme points of the numerical range of a quasihyponormal operator to be eigenvalues. It is also established that if T is bounded and there is IIxll = 1 such that IITxll = IITII and that and lt; Tx, x and gt; is a boundary point of the numerical range of T. then T has eigenvalues. Finally, an example is included of a paranormal operator which is not convexoid and such that T -∝ I is not paranormal for certain values of ∝. |
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