Professor Kraus will investigate some questions concerning tensor products and approximation properties of weakly closed subspaces of the algebra of bounded operators on a Hilbert space, and some similar questions for operator spaces. In particular, he will investigate the problem of whether all CSL algebras have a certain weak approximation property which guarantees that the algebras behave well under tensoring. Other projects involve the study of the class of groups whose associated von Neumann algebras have this approximation property, and the study of other related approximation properties. This project involves the study of operators on Hilbert spaces. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This research is an attempt to understand how algebras of these operators acting on independent Hilbert spaces behave when they are combined by taking the tensor product of these spaces.
