Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces

Detalhes bibliográficos
Autor(a) principal: Piccione,Paolo
Data de Publicação: 2005
Outros Autores: Tausk,Daniel V.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652005000400002
Resumo: We prove that any countable family of Lagrangian subspaces of a symplectic Hilbert space admits a common complementary Lagrangian. The proof of this puzzling result, which is not totally elementary also in the finite dimensional case, is obtained as an application of the spectral theorem for unbounded self-adjoint operators.
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spelling Complementary Lagrangians in infinite dimensional symplectic Hilbert spacessymplectic Hilbert spacesLagrangian subspacesLagrangian Grassmannianunbounded self-adjoint operatorsspectral theoremWe prove that any countable family of Lagrangian subspaces of a symplectic Hilbert space admits a common complementary Lagrangian. The proof of this puzzling result, which is not totally elementary also in the finite dimensional case, is obtained as an application of the spectral theorem for unbounded self-adjoint operators.Academia Brasileira de Ciências2005-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652005000400002Anais da Academia Brasileira de Ciências v.77 n.4 2005reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652005000400002info:eu-repo/semantics/openAccessPiccione,PaoloTausk,Daniel V.eng2005-11-29T00:00:00Zoai:scielo:S0001-37652005000400002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2005-11-29T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces
title Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces
spellingShingle Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces
Piccione,Paolo
symplectic Hilbert spaces
Lagrangian subspaces
Lagrangian Grassmannian
unbounded self-adjoint operators
spectral theorem
title_short Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces
title_full Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces
title_fullStr Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces
title_full_unstemmed Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces
title_sort Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces
author Piccione,Paolo
author_facet Piccione,Paolo
Tausk,Daniel V.
author_role author
author2 Tausk,Daniel V.
author2_role author
dc.contributor.author.fl_str_mv Piccione,Paolo
Tausk,Daniel V.
dc.subject.por.fl_str_mv symplectic Hilbert spaces
Lagrangian subspaces
Lagrangian Grassmannian
unbounded self-adjoint operators
spectral theorem
topic symplectic Hilbert spaces
Lagrangian subspaces
Lagrangian Grassmannian
unbounded self-adjoint operators
spectral theorem
description We prove that any countable family of Lagrangian subspaces of a symplectic Hilbert space admits a common complementary Lagrangian. The proof of this puzzling result, which is not totally elementary also in the finite dimensional case, is obtained as an application of the spectral theorem for unbounded self-adjoint operators.
publishDate 2005
dc.date.none.fl_str_mv 2005-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652005000400002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652005000400002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652005000400002
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.77 n.4 2005
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
instacron_str ABC
institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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