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020 _a9783031572012
_9978-3-031-57201-2
024 7 _a10.1007/978-3-031-57201-2
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
100 1 _aOertel, Frank.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984174
245 1 0 _aUpper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions
_h[electronic resource] /
_cby Frank Oertel.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXVI, 230 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2349
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 _aThis 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).
650 0 _aFunctional analysis.
650 0 _aProbabilities.
_965724
650 0 _aMathematical physics.
650 0 _aMathematical optimization.
_965522
650 1 4 _aFunctional Analysis.
650 2 4 _aProbability Theory.
_967428
650 2 4 _aMathematical Physics.
650 2 4 _aOptimization.
_965528
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031572005
776 0 8 _iPrinted edition:
_z9783031572029
830 0 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2349
_975434
856 4 0 _uhttps://doi.org/10.1007/978-3-031-57201-2
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c63318
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