  As part of the search for the value of the smallest upper bound of the best
constant for the famous Grothendieck inequality, the so-called Grothendieck
constant (a hard open problem - unsolved since 1953), we provide a further
approach, primarily built on functions which map correlation matrices entrywise
to correlation matrices by means of the Schur product, multivariate Gaussian
analysis, copulas and inversion of suitable Taylor series. We summarise first
results and point towards related open problems and topics for future research.
