{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1363107370906889856.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1017/s0305004100054670"}},{"identifier":{"@type":"URI","@value":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0305004100054670"}}],"dc:title":[{"@value":"Inequalities between means of positive operators"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p>One of the most fruitful – and natural – ways of introducing a partial order in the set of bounded self-adjoint operators in a Hilbert space <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004100054670_xs1D4D7\"/> is through the concept of a positive operator. A bounded self-adjoint operator <jats:italic>A</jats:italic> denned on <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004100054670_xs1D4D7\"/> is called positive – and one writes <jats:italic>A</jats:italic> ≥ 0 - if the inner product (ψ, <jats:italic>A</jats:italic>ψ) ≥ 0 for every ψ ∈ <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0305004100054670_xs1D4D7\"/>. If, in addition, (ψ, <jats:italic>A</jats:italic>ψ) = 0 only if ψ = 0, then A is called <jats:italic>positive-definite</jats:italic> and one writes <jats:italic>A</jats:italic> > 0. Further, if there exists a real number γ > 0 such that <jats:italic>A</jats:italic> — <jats:italic>γI</jats:italic> ≥ 0, <jats:italic>I</jats:italic> being the unit operator, then <jats:italic>A</jats:italic> is called <jats:italic>strictly positive</jats:italic> (in symbols, <jats:italic>A</jats:italic> ≫ 0). In a finite dimensional space, a positive-definite operator is also strictly positive.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1383107370906889857","@type":"Researcher","foaf:name":[{"@value":"K. V. Bhagwat"}]},{"@id":"https://cir.nii.ac.jp/crid/1383107370906889856","@type":"Researcher","foaf:name":[{"@value":"R. Subramanian"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"03050041"},{"@type":"EISSN","@value":"14698064"}],"prism:publicationName":[{"@value":"Mathematical Proceedings of the Cambridge Philosophical Society"}],"dc:publisher":[{"@value":"Cambridge University Press (CUP)"}],"prism:publicationDate":"1978-05","prism:volume":"83","prism:number":"3","prism:startingPage":"393","prism:endingPage":"401"},"reviewed":"false","dc:rights":["https://www.cambridge.org/core/terms"],"url":[{"@id":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0305004100054670"}],"createdAt":"2008-11-07","modifiedAt":"2019-05-27","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360588381060655872","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Estimations of Karcher mean by Hadamard product"}]},{"@id":"https://cir.nii.ac.jp/crid/1360849387446766208","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"On matrix inequalities between the power means: Counterexamples"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1017/s0305004100054670"},{"@type":"CROSSREF","@value":"10.1016/j.laa.2024.09.013_references_DOI_JI1sjXrv5Bh0BOhiA5gfSY4bkWC"},{"@type":"CROSSREF","@value":"10.1016/j.laa.2013.04.012_references_DOI_JI1sjXrv5Bh0BOhiA5gfSY4bkWC"}]}