The set of partial isometries as a quotient Finsler space

A known general program, designed to endow the quotient space UA/UB of the unitary groups UA, UB of the C∗ algebras B⊂A with an invariant Finsler metric, is applied to obtain a metric for the space I(H) of partial isometries of a Hilbert space H. I(H) is a quotient of the unitary group of B(H)×B(H),...

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Detalles Bibliográficos
Autor: Andruchow, Esteban
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/163816
Acceso en línea:http://hdl.handle.net/11336/163816
Access Level:acceso abierto
Palabra clave:PARTIAL ISOMETRIES
FINSLER METRIC
MINIMAL CURVES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:A known general program, designed to endow the quotient space UA/UB of the unitary groups UA, UB of the C∗ algebras B⊂A with an invariant Finsler metric, is applied to obtain a metric for the space I(H) of partial isometries of a Hilbert space H. I(H) is a quotient of the unitary group of B(H)×B(H), where B(H) is the algebra of bounded linear operators in H. Under this program, the solution of a linear best approximation problem leads to the computation of minimal geodesics in the quotient space. We find solutions of this best approximation problem, and study properties of the minimal geodesics obtained.