Operators which preserve a positive definite inner product

Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.

Detalles Bibliográficos
Autor principal: Andruchow, Esteban
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: Birkhauser Verlag AG 2024
Materias:
A-isometries
A-unitaries
Compatible subspaces
Symmetrizable transformations
Acceso en línea:http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1816
Aporte de:
Repositorio Institucional Digital de Acceso Abierto (UNGS) de Universidad Nacional de General Sarmiento
id I71-R177-UNGS-1816
record_format dspace
spelling I71-R177-UNGS-18162024-12-23T14:34:48Z Operators which preserve a positive definite inner product Andruchow, Esteban A-isometries A-unitaries Compatible subspaces Symmetrizable transformations 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. Let H be a Hilbert space, A a positive definite operator in H and hf, giA = hAf, gi, f, g ∈ H, the A-inner product. This paper studies the geometry of the set I a A := { adjointable isometries for h , iA}. It is proved that I a A is a submanifold of the Banach algebra of adjointable operators, and a homogeneous space of the group of invertible operators in H, which are unitaries for the A-inner product. Smooth curves in I a A with given initial conditions, which are minimal for the metric induced by h , iA, are presented. This result depends on an adaptation of M.G. Krein’s extension method of symmetric contractions, in order that it works also for symmetrizable transformations (i.e., operators which are selfadjoint for the A-inner product). 2024-12-23T14:30:41Z 2024-12-23T14:30:41Z 2022 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E. (2022). Operators which preserve a positive definite inner product. Integral Equations and Operator Theory, 94(3), 29, 1-22. 0378-620X http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1816 eng doi.org/10.1007/s00020-022-02709-0 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. 2022; 94(3): 29, 1-22 https://link.springer.com/journal/20/volumes-and-issues/94-3
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 A-isometries
A-unitaries
Compatible subspaces
Symmetrizable transformations
spellingShingle A-isometries
A-unitaries
Compatible subspaces
Symmetrizable transformations
Andruchow, Esteban
Operators which preserve a positive definite inner product
topic_facet A-isometries
A-unitaries
Compatible subspaces
Symmetrizable transformations
description Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
format Artículo
Artículo
publishedVersion
author Andruchow, Esteban
author_facet Andruchow, Esteban
author_sort Andruchow, Esteban
title Operators which preserve a positive definite inner product
title_short Operators which preserve a positive definite inner product
title_full Operators which preserve a positive definite inner product
title_fullStr Operators which preserve a positive definite inner product
title_full_unstemmed Operators which preserve a positive definite inner product
title_sort operators which preserve a positive definite inner product
publisher Birkhauser Verlag AG
publishDate 2024
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1816
work_keys_str_mv AT andruchowesteban operatorswhichpreserveapositivedefiniteinnerproduct
_version_ 1824528619974688768

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