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dc.contributor.author
Beltita, Daniel
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dc.contributor.author
Larotonda, Gabriel Andrés
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dc.date.available
2023-07-20T16:02:34Z
dc.date.issued
2023-01
dc.identifier.citation
Beltita, Daniel; Larotonda, Gabriel Andrés; Unitary group orbits versus groupoid orbits of normal operators; Springer; The Journal Of Geometric Analysis; 33; 3; 1-2023; 1-44
dc.identifier.issn
1050-6926
dc.identifier.uri
http://hdl.handle.net/11336/204675
dc.description.abstract
We study the unitary orbit of a normal operator a∈ B(H) , regarded as a homogeneous space for the action of unitary groups associated with symmetrically normed ideals of compact operators. We show with an unified treatment that the orbit is a submanifold of the various ambient spaces if and only if the spectrum of a is finite, and in that case, it is a closed submanifold. For arithmetically mean closed ideals, we show that nevertheless the orbit always has a natural manifold structure, modeled by the kernel of a suitable conditional expectation. When the spectrum of a is not finite, we describe the closure of the orbits of a for the different norm topologies involved. We relate these results to the action of the groupoid of partial isometries via the moment map given by the range projection of normal operators. We show that all these groupoid orbits also have differentiable structures for which the target map is a smooth submersion. For any normal operator a, we also describe the norm closure of its groupoid orbit Oa, which leads to necessary and sufficient spectral conditions on a ensuring that Oa is norm closed and that Oa is a closed embedded submanifold of B(H).
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
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dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
GROUPOID
dc.subject
NORMAL OPERATOR
dc.subject
OPERATOR IDEAL
dc.subject
UNITARY ORBIT
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Unitary group orbits versus groupoid orbits of normal operators
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-06-16T18:00:20Z
dc.journal.volume
33
dc.journal.number
3
dc.journal.pagination
1-44
dc.journal.pais
Alemania
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dc.journal.ciudad
Berlin
dc.description.fil
Fil: Beltita, Daniel. Institute Of Mathematics "simion Stoilow" Of The Romanian Academy.; Rumania
dc.description.fil
Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.journal.title
The Journal Of Geometric Analysis
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s12220-022-01187-5
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1007/s12220-022-01187-5
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