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Unified min-max and interlacing theorems for linear operators

2011Journal article Open access
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dc.contributor.authorIglésias, Laura
dc.contributor.authorSanta-Clara, Catarina
dc.contributor.authorSilva, Fernando C.
dc.date.accessioned2013-02-17T13:47:23Z
dc.date.available2013-02-17T13:47:23Z
dc.date.issued2011
dc.description.abstractThere exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.por
dc.identifier.citationIGLESIAS, Laura; SANTA-CLARA, Catarina; SILVA, Fernando C. - Unified min-max and interlacing theorems for linear operators. Linear & Multilinear Algebra. ISSN 0308-1087. Vol. 59, n.º 6 (2011) p. 651-669.por
dc.identifier.issn0308-1087
dc.identifier.urihttp://hdl.handle.net/10400.21/2258
dc.language.isoengpor
dc.peerreviewedyespor
dc.publisherTaylor & Francis LTDpor
dc.subjectGoldie Dimensionpor
dc.subjectModular Latticepor
dc.subjectEigenvaluespor
dc.subjectInvariant Factorspor
dc.subjectCompact Operatorspor
dc.subjectInfinite Goldie-Dimensionpor
dc.titleUnified min-max and interlacing theorems for linear operatorspor
dc.typejournal article
dspace.entity.typePublication
oaire.citation.conferencePlaceOxonpor
oaire.citation.endPage669por
oaire.citation.issue6por
oaire.citation.startPage651por
oaire.citation.titleLinear & Multilinear Algebrapor
oaire.citation.volume59por
person.familyNameIglésias
person.givenNameLaura
person.identifier.orcid0000-0003-0473-4557
rcaap.rightsrestrictedAccesspor
rcaap.typearticlepor
relation.isAuthorOfPublication3f1f700e-295e-4de1-a2d6-62a41bbd8671
relation.isAuthorOfPublication.latestForDiscovery3f1f700e-295e-4de1-a2d6-62a41bbd8671

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