Title: The Cotlar-Stein Lemma, Grothendiecks Inequality and All That Show Chinese title

Title: 柯特拉-斯坦引理，格罗滕迪克不等式及其它

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. Show Chinese abstract

Abstract: 本文的目的是指出散射理论、双算子积分、Krein谱移函数、积分理论、双测度、费曼路径积分、调和分析和泛函分析以及自过去50年以来在量子物理中的许多其他应用之间的联系。 起点是Kluvanek的积分结构，他希望将其应用于量子物理，并且现在由于许多作者的贡献，尤其是 intervening 年间的前苏联数学物理学家，已开始结出成果。 很快，可能证明存在满足Wightman公理的四维时空实用量子场论。 这是其中一项Clay奖的目标。 目前，仅在少于四维时空的模型中存在玩具模型。