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Upper bounds for Grothendieck consta...

Oertel, Frank.

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Upper bounds for Grothendieck constants, quantum correlation matrices and CCP functions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Upper bounds for Grothendieck constants, quantum correlation matrices and CCP functions/ by Frank Oertel.
Author:	Oertel, Frank.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	xvi, 230 p. :ill., digital ;24 cm.
[NT 15003449]:	- Introduction and motivation -- Complex Gaussian random vectors and their probability law -- A quantum correlation matrix version of the Grothendieck inequality -- Powers of inner products of random vectors, uniformly distributed on the sphere -- Completely correlation preserving functions -- The real case: towards extending Krivine's approach -- The complex case: towards extending Haagerup's approach -- A summary scheme of the main result -- Concluding remarks and open problems -- References -- Index.
Contained By:	Springer Nature eBook
Subject:	Mathematical constants. -
Online resource:	https://doi.org/10.1007/978-3-031-57201-2
ISBN:	9783031572012

Upper bounds for Grothendieck constants, quantum correlation matrices and CCP functions
Oertel, Frank.

Upper bounds for Grothendieck constants, quantum correlation matrices and CCP functions[electronic resource] /by Frank Oertel. - Cham :Springer Nature Switzerland :2024. - xvi, 230 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23491617-9692 ;. - Lecture notes in mathematics ;v. 2349..

- Introduction and motivation -- Complex Gaussian random vectors and their probability law -- A quantum correlation matrix version of the Grothendieck inequality -- Powers of inner products of random vectors, uniformly distributed on the sphere -- Completely correlation preserving functions -- The real case: towards extending Krivine's approach -- The complex case: towards extending Haagerup's approach -- A summary scheme of the main result -- Concluding remarks and open problems -- References -- Index.

This book concentrates on the famous Grothendieck inequality and the continued search for the still unknown best possible value of the real and complex Grothendieck constant (an open problem since 1953) It describes in detail the state of the art in research on this fundamental inequality, including Krivine's recent contributions, and sheds light on related questions in mathematics, physics and computer science, particularly with respect to the foundations of quantum theory and quantum information theory. Unifying the real and complex cases as much as possible, the monograph introduces the reader to a rich collection of results in functional analysis and probability. In particular, it includes a detailed, self-contained analysis of the multivariate distribution of complex Gaussian random vectors. The notion of Completely Correlation Preserving (CCP) functions plays a particularly important role in the exposition. The prerequisites are a basic knowledge of standard functional analysis, complex analysis, probability, optimisation and some number theory and combinatorics. However, readers missing some background will be able to consult the generous bibliography, which contains numerous references to useful textbooks. The book will be of interest to PhD students and researchers in functional analysis, complex analysis, probability, optimisation, number theory and combinatorics, in physics (particularly in relation to the foundations of quantum mechanics) and in computer science (quantum information and complexity theory)

ISBN: 9783031572012

Standard No.: 10.1007/978-3-031-57201-2doiSubjects--Topical Terms:

578742
Mathematical constants.

LC Class. No.: QA320

Dewey Class. No.: 515.7

Upper bounds for Grothendieck constants, quantum correlation matrices and CCP functions
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505 0 $a - Introduction and motivation -- Complex Gaussian random vectors and their probability law -- A quantum correlation matrix version of the Grothendieck inequality -- Powers of inner products of random vectors, uniformly distributed on the sphere -- Completely correlation preserving functions -- The real case: towards extending Krivine's approach -- The complex case: towards extending Haagerup's approach -- A summary scheme of the main result -- Concluding remarks and open problems -- References -- Index.
520 $a This book concentrates on the famous Grothendieck inequality and the continued search for the still unknown best possible value of the real and complex Grothendieck constant (an open problem since 1953) It describes in detail the state of the art in research on this fundamental inequality, including Krivine's recent contributions, and sheds light on related questions in mathematics, physics and computer science, particularly with respect to the foundations of quantum theory and quantum information theory. Unifying the real and complex cases as much as possible, the monograph introduces the reader to a rich collection of results in functional analysis and probability. In particular, it includes a detailed, self-contained analysis of the multivariate distribution of complex Gaussian random vectors. The notion of Completely Correlation Preserving (CCP) functions plays a particularly important role in the exposition. The prerequisites are a basic knowledge of standard functional analysis, complex analysis, probability, optimisation and some number theory and combinatorics. However, readers missing some background will be able to consult the generous bibliography, which contains numerous references to useful textbooks. The book will be of interest to PhD students and researchers in functional analysis, complex analysis, probability, optimisation, number theory and combinatorics, in physics (particularly in relation to the foundations of quantum mechanics) and in computer science (quantum information and complexity theory)
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