Operator Least Squares Problems and Moore–Penrose Inverses in Krein Spaces

Given a Krein space H and B, C in L(H), L(H), the bounded linear operators on H, the minimization/maximization of expressions of the form (BX−C)#(BX−C) as X runs over L(H) is studied. Complete solutions are found for the problems posed, including solvability criteria and a characterization of the so...

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Detalles Bibliográficos
Autores: Contino, Maximiliano, Maestripieri, Alejandra Laura, Marcantognini Palacios, Stefania Alma María
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/88408
Acceso en línea:http://hdl.handle.net/11336/88408
Access Level:acceso abierto
Palabra clave:OPERATOR APPROXIMATION
KREIN SPACES
MOORE-PENROSE INVERSES
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Given a Krein space H and B, C in L(H), L(H), the bounded linear operators on H, the minimization/maximization of expressions of the form (BX−C)#(BX−C) as X runs over L(H) is studied. Complete solutions are found for the problems posed, including solvability criteria and a characterization of the solutions when they exist. Min-max problems associated to Krein space decompositions of B are also considered, leading to a characterization of the Moore-Penrose inverse as the unique solution of a variational problem. Other generalized inverses are similarly described.