Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions

Frank Oertel is an Honorary Research Associate at the LSE Centre for Philosophy of Natural and Social Science (CPNSS) in London. After studying mathematics and physics at the University of Kaiserslautern-Landau (RPTU), he was a researcher at the University of Zurich, ETH Zurich and Heriot-Watt University, Edinburgh and a lecturer at University College Cork (UCC), Ireland and the University of Southampton, UK. His research interests are primarily in functional analysis, including its applications to quantum mechanics, and applications of functional and stochastic analysis to problems in financial mathematics. He has also worked as a mathematical advisor in the financial industry, including banking supervision and audit (Frankfurt, Zurich, Bonn, Munich and London).

- 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.