Title

Generalizations and extensions of the Grothendieck inequality

Date of Completion

January 2007

Keywords

Mathematics

Degree

Ph.D.

Abstract

Integration of scalar-valued functions with respect to Fréchet measures (which are also known as Fn-measures or multi-measures) has been undertaken by different authors (see Blei [4,5] or Dobrakov [11-13]). In this paper we will follow the notations and conventions adopted in [5]. The purpose of this paper is to show that an inner product of vector-valued functions can be integrated with respect to a bimeasure (F 2-measure) iteratively, in a way similar to the integration of tensor products of scalar-valued functions. We will then use this theory to generalize the Grothendieck inequality to a continuous framework.^