Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
In the present paper, we study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U(K+C) of the unitization of the compact operators K(H) + C, or equivalently, the quotient U(K+C) /U(D(K+C)) . We relate this and the action...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2021 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/157556 |
| Acesso em linha: | http://hdl.handle.net/11336/157556 |
| Access Level: | Acceso aberto |
| Palavra-chave: | UNITARY ORBITS GEODESIC CURVES MINIMALITY FINSLER METRICS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | In the present paper, we study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U(K+C) of the unitization of the compact operators K(H) + C, or equivalently, the quotient U(K+C) /U(D(K+C)) . We relate this and the action of different unitary subgroups to describe metric geodesics (using a natural distance) which join end points. As a consequence we obtain a local Hopf-Rinow theorem. We also explore cases about the uniqueness of short curves and prove that there exist some of these that cannot be parameterized using minimal anti-Hermitian operators of K(H) + C. |
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