Show simple item record

dc.contributor.advisorMisra, Gadadhar
dc.contributor.authorRay, Samya Kumar
dc.date.accessioned2016-06-20T07:01:17Z
dc.date.accessioned2018-07-31T06:09:04Z
dc.date.available2016-06-20T07:01:17Z
dc.date.available2018-07-31T06:09:04Z
dc.date.issued2016-06-20
dc.date.submitted2012
dc.identifier.urihttps://etd.iisc.ac.in/handle/2005/2540
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/3295/G25612-Abs.pdfen_US
dc.description.abstractGrothendieck published an extraordinary paper entitled ”Resume de la theorie metrique des pro¬duits tensoriels topologiques” in 1953. The main result of this paper is the inequality which is commonly known as Grothendieck Inequality. Following Kirivine, in this article, we give the proof of Grothendieck Inequality. We refor¬mulate it in different forms. We also investigate the famous Grothendieck constant KG. The Grothendieck constant was achieved by taking supremum over a special class of matrices. But our attempt will be to investigate it, considering a smaller class of matrices, namely only the positive definite matrices in this class. Actually we want to use it to get a counterexample of Matsaev’s conjecture, which was proved to be right by Von Neumann in some specific cases. In chapter 1, we shall state and prove the Grothendieck Inequality. In chapter 2, we shall introduce tensor product of vector spaces and different tensor norms. In chapter 3, we shall formulate Grothendieck Inequality in different forms and use the notion of tensor norms for its equivalent formation .In the last chapteri.ein chapter4we shall investigate on the Grothendieck constant.en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG25612en_US
dc.subjectInequalities (Mathenatics)en_US
dc.subjectGrothendieck Inequalitiesen_US
dc.subjectVector Spacesen_US
dc.subjectGrothendieck Constanten_US
dc.subjectTensor Normsen_US
dc.subjectTensor Productsen_US
dc.subjectGrothendieck Inequalityen_US
dc.subject.classificationAlgebraen_US
dc.titleGrothendieck Inequalityen_US
dc.typeThesisen_US
dc.degree.nameMSen_US
dc.degree.levelMastersen_US
dc.degree.disciplineFaculty of Scienceen_US


Files in this item

This item appears in the following Collection(s)

Show simple item record