NORMED UNIFORMLY REFLEXIVE STRUCTURES Henk Barendregt Mathematisch Instituut

Normed uniformly reflexive structures

Abstract Cauchy problems and stochastic integral equations

Cauchy problems and stochastic integral equations Bachelor thesis, June 21, 2011 Thesis supervisor: dr. O. van Gaans Mathematisch Instituut, Universiteit Leiden

On Henk Barendregt’s Favorite Open Problem

H is the λ-theory extending β-conversion by identifying all closed unsolvables. A long-standing open problem of H. Barendregt states that the range property holds in H. Here we discuss what we know about the problem. We also make some remarks on the λ-theory Hω (the closure of H under the ω-rule and β-conversion).

Duality and hidden symmetries in interacting particle systems

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the “hidden” symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of S...

Uniformly convex Banach spaces are reflexive - constructively

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the MilmanPettis theorem that uniformly convex Banach spaces are reflexive. Our aim in this note is to present a fully constructive analysis of the Milman-Pettis theorem [11, 12, 9, 13]: a uniformly convex Banach space is reflexive. First, t...