p-Schatten commutators of projections
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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| Formato: | Artículo publishedVersion |
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Birkhauser
2024
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1819 |
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I71-R177-UNGS-1819 |
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I71-R177-UNGS-18192024-12-23T14:30:42Z p-Schatten commutators of projections Andruchow, Esteban Di Iorio y Lucero, María Eugenia Projections Schatten P-Ideals Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina. Fil: Di Iorio y Lucero, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina. Let H= H+? H- be a fixed orthogonal decomposition of the complex separable Hilbert space H in two infinite-dimensional subspaces. We study the geometry of the set Pp of selfadjoint projections in the Banach algebra Ap= { A? B(H) : [A, E+] ? Bp(H) } , where E+ is the projection onto H+ and Bp(H) is the Schatten ideal of p-summable operators (1 ? p< ?). The norm in Ap is defined in terms of the norms of the matrix entries of the operators given by the above decomposition. The space Pp is shown to be a differentiable C? submanifold of Ap, and a homogeneous space of the group of unitary operators in Ap. The connected components of Pp are characterized, by means of a partition of Pp in nine classes, four discrete classes, and five essential classes: (1) the first two corresponding to finite rank or co-rank, with the connected components parametrized by these ranks; (2) the next two discrete classes carrying a Fredholm index, which parametrizes their components; (3) the remaining essential classes, which are connected. 2024-12-23T14:30:42Z 2024-12-23T14:30:42Z 2021 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E. y Di Iorio y Lucero, M. E. (2021). p-Schatten commutators of projections. Annals of Functional Analysis, 12(2), 1-20. 2008-8752 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1819 eng http://dx.doi.org/10.1007/s43034-021-00116-x info:eu-repo/semantics/restrictedAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Birkhauser Annals of Functional Analysis. 2021; 12(2): 1-20 https://link.springer.com/journal/43034/volumes-and-issues/12-2 |
| 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 |
Projections Schatten P-Ideals |
| spellingShingle |
Projections Schatten P-Ideals Andruchow, Esteban Di Iorio y Lucero, María Eugenia p-Schatten commutators of projections |
| topic_facet |
Projections Schatten P-Ideals |
| description |
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. |
| format |
Artículo Artículo publishedVersion |
| author |
Andruchow, Esteban Di Iorio y Lucero, María Eugenia |
| author_facet |
Andruchow, Esteban Di Iorio y Lucero, María Eugenia |
| author_sort |
Andruchow, Esteban |
| title |
p-Schatten commutators of projections |
| title_short |
p-Schatten commutators of projections |
| title_full |
p-Schatten commutators of projections |
| title_fullStr |
p-Schatten commutators of projections |
| title_full_unstemmed |
p-Schatten commutators of projections |
| title_sort |
p-schatten commutators of projections |
| publisher |
Birkhauser |
| publishDate |
2024 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1819 |
| work_keys_str_mv |
AT andruchowesteban pschattencommutatorsofprojections AT diiorioyluceromariaeugenia pschattencommutatorsofprojections |
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1824528700056535040 |