Schmidt decomposable products of projections
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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Birkhauser Verlag Ag
2024
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1821 |
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I71-R177-UNGS-1821 |
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I71-R177-UNGS-18212024-12-23T14:31:44Z Schmidt decomposable products of projections Andruchow, Esteban Corach, Gustavo Projections Products of projections Differences of projections 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: Corach, Gustavo. Universidad Nacional de General Sarmiento; Instituto de Ciencias; Argentina. Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina. We characterize operators T = P Q (P, Q orthogonal projections in a Hilbert space H) which have a singular value decomposition. A spatial characterizations is given: this condition occurs if and only if there exist orthonormal bases {ψn} of R(P) and {ξn} of R(Q) such that ξn, ψm = 0 if n = m. Also it is shown that this is equivalent to A = P − Q being diagonalizable. Several examples are studied, relating Toeplitz, Hankel and Wiener–Hopf operators to this condition. We also examine the relationship with the differential geometry of the Grassmann manifold of underlying the Hilbert space: if T = P Q has a singular value decomposition, then the generic parts of P and Q are joined by a minimal geodesic with diagonalizable exponent. 2024-12-23T14:30:42Z 2024-12-23T14:30:42Z 2017 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Corach, G. y Andruchow, E. (2017). Schmidt Decomposable Products of Projections. Integral Equations and Operator Theory, 89(4), 557-580. 0378-620X http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1821 eng info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Birkhauser Verlag Ag Integral Equations and Operator Theory. Dic. 2017; 89(4): 557-580 |
| 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 Products of projections Differences of projections |
| spellingShingle |
Projections Products of projections Differences of projections Andruchow, Esteban Corach, Gustavo Schmidt decomposable products of projections |
| topic_facet |
Projections Products of projections Differences of projections |
| description |
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. |
| format |
Artículo Artículo publishedVersion |
| author |
Andruchow, Esteban Corach, Gustavo |
| author_facet |
Andruchow, Esteban Corach, Gustavo |
| author_sort |
Andruchow, Esteban |
| title |
Schmidt decomposable products of projections |
| title_short |
Schmidt decomposable products of projections |
| title_full |
Schmidt decomposable products of projections |
| title_fullStr |
Schmidt decomposable products of projections |
| title_full_unstemmed |
Schmidt decomposable products of projections |
| title_sort |
schmidt decomposable products of projections |
| publisher |
Birkhauser Verlag Ag |
| publishDate |
2024 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1821 |
| work_keys_str_mv |
AT andruchowesteban schmidtdecomposableproductsofprojections AT corachgustavo schmidtdecomposableproductsofprojections |
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1824528700471771136 |