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Please use this identifier to cite or link to this item: http://etd.iisc.ernet.in/2005/2540

Title: Grothendieck Inequality
Authors: Ray, Samya Kumar
Advisors: Misra, Gadadhar
Keywords: Inequalities (Mathenatics)
Grothendieck Inequalities
Vector Spaces
Grothendieck Constant
Tensor Norms
Tensor Products
Grothendieck Inequality
Submitted Date: Dec-2012
Series/Report no.: G25612
Abstract: Grothendieck 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.
Abstract file URL: http://etd.ncsi.iisc.ernet.in/abstracts/3295/G25612-Abs.pdf
URI: http://etd.iisc.ernet.in/handle/2005/2540
Appears in Collections:Mathematics (math)

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