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dc.contributor.author
Andruchow, Esteban
dc.contributor.author
Chiumiento, Eduardo Hernan
dc.contributor.author
Di Iorio y Lucero, María Eugenia
dc.date.available
2017-06-26T20:39:11Z
dc.date.issued
2015-12
dc.identifier.citation
Andruchow, Esteban; Chiumiento, Eduardo Hernan; Di Iorio y Lucero, María Eugenia; Proper subspaces and compatibility; Polish Acad Sciences Inst Mathematics; Studia Mathematica; 231; 3; 12-2015; 195-218
dc.identifier.issn
0039-3223
dc.identifier.uri
http://hdl.handle.net/11336/18930
dc.description.abstract
Let E be a Banach space contained in a Hilbert space L. Assume thatthe inclusion is continuous with dense range. Following the terminology of Gohberg andZambicki, we say that a bounded operator on E is a proper operator if it admits anadjoint with respect to the inner product of L. A proper operator which is self-adjointwith respect to the inner product of L is called symmetrizable. By a proper subspace Swe mean a closed subspace of E which is the range of a proper projection. Furthermore,if there exists a symmetrizable projection onto S, then S belongs to a well-known class ofsubspaces called compatible subspaces. We nd equivalent conditions to describe propersubspaces. Then we prove a necessary and sucient condition for a proper subspace tobe compatible. The existence of non-compatible proper subspaces is related to spectralproperties of symmetrizable operators. Each proper subspace S has a supplement T whichis also a proper subspace.We give a characterization of the compatibility of both subspacesS and T . Several examples are provided that illustrate dierent situations between properand compatible subspaces
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Polish Acad Sciences Inst Mathematics
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Projection
dc.subject
Compatible Subspace
dc.subject
Proper Operator
dc.subject
Spectrum
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Proper subspaces and compatibility
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-06-26T19:51:10Z
dc.journal.volume
231
dc.journal.number
3
dc.journal.pagination
195-218
dc.journal.pais
Polonia
dc.journal.ciudad
Varsovia
dc.description.fil
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
dc.description.fil
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
dc.description.fil
Fil: Di Iorio y Lucero, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
dc.journal.title
Studia Mathematica
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/ 10.4064/sm8225-2-2016
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/231/3/91441/proper-subspaces-and-compatibility
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1503.00596


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