Index of Faithful Normal Conditional Expectations

Representation of faithful normal expectations in von Neumann algebras

Normal Conditional Expectations of Finite Index and Sets of Modular Generators

Normal conditional expectations E : M → N ⊆ M of finite index on von Neumann algebras M with discrete center are investigated to find an estimate for the minimal number of generators of M as a Hilbert N-module. Analyzing the case of M being finite type I with discrete center we obtain that these von Neumann algebras M are always finitely generated projective N-modules with a minimal generator s...

Normal conditional expectations of finite index and sets of module generators

Normal conditional expectations E : M → N ⊆ M of finite index on von Neumann algebras M with discrete center are investigated to find an estimate for the minimal number of generators of M as a Hilbert N -module. Analyzing the case of M being finite type I with discrete center we obtain that these von Neumann algebras M are always finitely generated projective N -modules with a minimal generator...

Conditional Expectations and Renormalization

In optimal prediction methods one estimates the future behavior of underresolved systems by solving reduced systems of equations for expectations conditioned by partial data; renormalization group methods reduce the number of variables in complex systems through integration of unwanted scales. We establish the relation between these methods for systems in thermal equilibrium, and use this relat...

The Specification of Conditional Expectations

This paper explores different speciÞcations of conditional expectations. The most common speciÞcation, linear least squares, is contrasted with nonparametric techniques that make no assumptions about the distribution of the data. Nonparametric regression is successful in capturing some nonlinearities in Þnancial data, in particular, asymmetric responses of security returns to the direction and ...