Unitary subgroups and orbits of compact self-adjoint operators
Revista con referato
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Polish Academy of Sciences. Institute of Mathematics
2025
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2152 |
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I71-R177-UNGS-2152 |
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I71-R177-UNGS-21522025-03-13T17:50:00Z Unitary subgroups and orbits of compact self-adjoint operators Bottazzi, Tamara Paula Varela, Alejandro Unitary Groups Lie Subgroups Unitary Orbits Geodesic Curves Minimal Operators in Quotient Spaces Matemáticas Matemática Pura Revista con referato Fil: Bottazzi, Tamara Paula. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Fil: Bottazzi, Tamara Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática Alberto Calderón; Argentina. Fil: Varela, Alejandro. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Sea H un espacio de Hilbert separable, y sean D(B(H) ah) los operadores diagonales acotados antihermíticos en alguna base ortonormal fija y K(H) los operadores compactos. Estudiamos el grupo de operadores unitarios Uk,d = {u ? U(H) : ?D ? D(B(H) ah), u ? e D ? K(H)} para obtener una descripción concreta de curvas cortas en órbitas unitarias de Fredholm Ob = {e Kbe?K : K ? K(H) ah} de un operador autoadjunto compacto b con multiplicidad espectral uno. Consideramos la distancia rectificable en Ob definida como el ínfimo de longitudes de curva medidas con la métrica de Finsler definida por medio del espacio cociente K(H) ah/D(K(H) ah). Entonces, para cada c ? Ob y x ? Tc(Ob) existe una elevación mínima Z0 ? B(H) ah (en la norma del cociente, no necesariamente compacta) tal que ?(t) = e tZ0 ce?tZ0 es una curva corta en Ob en un cierto intervalo. Let H be a separable Hilbert space, and let D(B(H) ah) be the antiHermitian bounded diagonal operators in some fixed orthonormal basis and K(H) the compact operators. We study the group of unitary operators Uk,d = {u ? U(H) : ?D ? D(B(H) ah), u ? e D ? K(H)} in order to obtain a concrete description of short curves in unitary Fredholm orbits Ob = {e Kbe?K : K ? K(H) ah} of a compact self-adjoint operator b with spectral multiplicity one. We consider the rectifiable distance on Ob defined as the infimum of curve lengths measured with the Finsler metric defined by means of the quotient space K(H) ah/D(K(H) ah). Then for every c ? Ob and x ? Tc(Ob) there exists a minimal lifting Z0 ? B(H) ah (in the quotient norm, not necessarily compact) such that ?(t) = e tZ0 ce?tZ0 is a short curve on Ob in a certain interval. Seja H um espaço de Hilbert separável, e sejam D(B(H) ah) os operadores diagonais limitados anti-Hermitianos em alguma base ortonormal fixa e K(H) os operadores compactos. Estudamos o grupo de operadores unitários Uk,d = {u ? U(H) : ?D ? D(B(H) ah), u ? e D ? K(H)} para obter uma descrição concreta de curvas curtas em órbitas de Fredholm unitárias Ob = {e Kbe?K : K ? K(H) ah} de um operador autoadjunto compacto b com multiplicidade espectral um. Consideramos a distância retificável em Ob definida como o ínfimo de comprimentos de curva medidos com a métrica de Finsler definida por meio do espaço quociente K(H) ah/D(K(H) ah). Então, para cada c ? Ob e x ? Tc(Ob), existe um levantamento mínimo Z0 ? B(H) ah (na norma quociente, não necessariamente compacto) tal que ?(t) = e tZ0 ce?tZ0 é uma curva curta em Ob em um determinado intervalo. 2025-03-13T17:50:00Z 2025-03-13T17:50:00Z 2017 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Bottazzi, T. P. y Varela, A. (2017). Unitary subgroups and orbits of compact self-adjoint operators. Studia Mathematica, 238(2), 55-176. 0039-3223 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2152 eng http://dx.doi.org/10.4064/sm8690-12-2016 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Polish Academy of Sciences. Institute of Mathematics Studia Mathematica. May. 2017; 238(2): 55-176 |
| institution |
Universidad Nacional de General Sarmiento |
| institution_str |
I-71 |
| repository_str |
R-177 |
| collection |
Repositorio Institucional Digital de Acceso Abierto (UNGS) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Unitary Groups Lie Subgroups Unitary Orbits Geodesic Curves Minimal Operators in Quotient Spaces Matemáticas Matemática Pura |
| spellingShingle |
Unitary Groups Lie Subgroups Unitary Orbits Geodesic Curves Minimal Operators in Quotient Spaces Matemáticas Matemática Pura Bottazzi, Tamara Paula Varela, Alejandro Unitary subgroups and orbits of compact self-adjoint operators |
| topic_facet |
Unitary Groups Lie Subgroups Unitary Orbits Geodesic Curves Minimal Operators in Quotient Spaces Matemáticas Matemática Pura |
| description |
Revista con referato |
| format |
Artículo Artículo publishedVersion |
| author |
Bottazzi, Tamara Paula Varela, Alejandro |
| author_facet |
Bottazzi, Tamara Paula Varela, Alejandro |
| author_sort |
Bottazzi, Tamara Paula |
| title |
Unitary subgroups and orbits of compact self-adjoint operators |
| title_short |
Unitary subgroups and orbits of compact self-adjoint operators |
| title_full |
Unitary subgroups and orbits of compact self-adjoint operators |
| title_fullStr |
Unitary subgroups and orbits of compact self-adjoint operators |
| title_full_unstemmed |
Unitary subgroups and orbits of compact self-adjoint operators |
| title_sort |
unitary subgroups and orbits of compact self-adjoint operators |
| publisher |
Polish Academy of Sciences. Institute of Mathematics |
| publishDate |
2025 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2152 |
| work_keys_str_mv |
AT bottazzitamarapaula unitarysubgroupsandorbitsofcompactselfadjointoperators AT varelaalejandro unitarysubgroupsandorbitsofcompactselfadjointoperators |
| _version_ |
1826997433506201600 |