The Cotlar-Stein Lemma, Grothendiecks Inequality and All That

Abstract

The purpose of this paper is point out connections between scattering theory, double operator integrals, Kreins spectral shift function, integration theory, bimeasures, Feynman path integrals, harmonic and functional analysis and many other applications to quantum physics made since the last 50 years or so. The starting point is Kluvaneks Integration Structures which he hoped to apply to quantum physics and is now bearing fruit from the contributions of many authors, especially former Soviet mathematical physicists in the intervening years. Soon, a practical quantum field theory in four space-time dimensions satisfying the Wightman axioms may be proved to exist. This is the aim of one of the Clay Prizes. At the moment, only toy models exist in fewer than four space-time dimensions.