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dc.contributor.author
Andruchow, Esteban
dc.contributor.author
Corach, Gustavo
dc.contributor.author
Mbekhta, Mostafa
dc.date.available
2015-08-14T21:14:49Z
dc.date.issued
2013-12
dc.identifier.citation
Andruchow, Esteban; Corach, Gustavo; Mbekhta, Mostafa; A geometry for split operators; Springer; Integral Equations and Operator Theory; 77; 4; 12-2013; 559-579
dc.identifier.issn
0378-620X
dc.identifier.uri
http://hdl.handle.net/11336/1691
dc.description.abstract
We study the set X of split operators acting in the Hilbert space H: X = {T ∈ B(H) : N(T) ∩ R(T) = {0} and N(T) + R(T) = H}. Inside X , we consider the set Y: Y = {T ∈ X : N(T) ⊥ R(T)}. Several characterizations of these sets are given. For instance T ∈ X if and only if there exists an oblique projection Q whose range is N(T) such that T + Q is invertible, if and only if T posseses a commuting (necessarilly unique) pseudo-inverse S (i.e. T S = ST,TST = T and STS = S). Analogous characterizations are given for Y. Two natural maps are considered: q : X → Q := {oblique projections in H}, q(T) = PR(T )//N(T ) and p : Y → P := {orthogonal projections in H}, p(T) = PR(T ), where PR(T )//N(T ) denotes the projection onto R(T) with nullspace N(T), and PR(T ) denotes the orthogonal projection onto R(T). These maps are in general non continuous, subsets of continuity are studied. For the map q these are: similarity orbits, and the subsets Xck ⊂ X of operators with rank k < ∞, and XFk ⊂ X of Fredholm operators with nullity k < ∞. For the map p there are analogous results. We show that the interior of X is XF0 ∪ XF1 , and that Xck and XFk are arc-wise connected differentiable manifolds.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Split Operator
dc.subject
Oblique Projection
dc.subject
Projections Pseudo-Inverses
dc.subject
Group Inverse Operators
dc.subject
Ep Operators
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
A geometry for split operators
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-03-30 10:35:44.97925-03
dc.identifier.eissn
1420-8989
dc.journal.volume
77
dc.journal.number
4
dc.journal.pagination
559-579
dc.journal.pais
Alemania
dc.journal.ciudad
Berlín
dc.description.fil
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
dc.description.fil
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
dc.description.fil
Fil: Mbekhta, Mostafa. Unité de Formation et de Recherche de Mathématiques. Université de Lille; Francia;
dc.journal.title
Integral Equations and Operator Theory
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00020-013-2086-9
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs00020-013-2086-9
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00020-013-2086-9


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