Proper subspaces and compatibility

Authors
Andruchow, Esteban; Chiumiento, Eduardo Hernan; Di Iorio y Lucero, María Eugenia
Publication Year
2015
Language
English
Format
article
Status
Published version
Description
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
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
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
Subject
PROJECTION
COMPATIBLE SUBSPACE
PROPER OPERATOR
SPECTRUM
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Open access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/18930