Schmidt decomposable products of projections

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dc.creator Andruchow, Esteban
dc.creator Corach, Gustavo
dc.date.accessioned 2024-12-23T14:30:42Z
dc.date.available 2024-12-23T14:30:42Z
dc.date.issued 2017
dc.identifier.citation Corach, G. y Andruchow, E. (2017). Schmidt Decomposable Products of Projections. Integral Equations and Operator Theory, 89(4), 557-580.
dc.identifier.issn 0378-620X
dc.identifier.uri http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1821
dc.description Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
dc.description Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
dc.description Fil: Corach, Gustavo. Universidad Nacional de General Sarmiento; Instituto de Ciencias; Argentina.
dc.description Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
dc.description.abstract 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.
dc.format application/pdf
dc.language eng
dc.publisher Birkhauser Verlag Ag
dc.rights info:eu-repo/semantics/openAccess
dc.rights https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.source Integral Equations and Operator Theory. Dic. 2017; 89(4): 557-580
dc.subject Projections
dc.subject Products of projections
dc.subject Differences of projections
dc.title Schmidt decomposable products of projections
dc.type info:eu-repo/semantics/article
dc.type info:ar-repo/semantics/artículo
dc.type info:eu-repo/semantics/publishedVersion


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