Special Session:
Analysis

Organizers: David Preiss (Warwick) and Ray Ryan (NUI, Galway)

This special session is followed by the Operator Theory and Real Analysis Splinter Group on both afternoons.

Tuesday, April 7 2009

14:15 - 15:10    Cairnes Lecture Theatre

Ivan Todorov (Queen's University Belfast):
Stable isomorphism of dual operator spaces

Two dual operator spaces X and Y are said to be stably isomorphic if the dual operator spaces obtained from X and Y after tensoring with the space B(H) of all bounded operators on a Hilbert space H are completely isometric and weak* homeomorphic. The notion of stable isomorphism, which is coarser than that of isomorphism, is closely related to the notion of Morita equivalence. In this talk, we present necessary and sufficient conditions for stable isomorphism of two dual operator spaces in terms of ternary rings of operators, that is, operator spaces closed under the triple product (a,b,c)\rightarrow ab^*c. We describe some applications of the results to the theory of dual operator algebras and present some examples motivated by the theory of CSL algebras.

15:15 - 16:10    Cairnes Lecture Theatre

Marianna Csőrnyei (UC London):
Differentiability of Lipschitz functions and other problems in geometric measure theory

Our main goal in this talk is to describe non-differentiability sets of Lipschitz functions on {\mathbb R}^n. This will lead us to the notion of tangent fields to null sets, and provide a new understanding of the structure of sets of small measure. This is a joint work with G. Alberti and D. Preiss.

Wednesday, April 8 2009

14:15 - 15:10    Cairnes Lecture Theatre

Stephen Gardiner (UCD):
Harmonic functions outside a cylinder

Several apparently different problems have recently led to consideration of harmonic functions in the complement of an infinite cylinder. It turns out that, in three dimensions, estimates for the Dirichlet problem and the Green function in this context are quite delicate. This talk will describe the motivation for studying such questions as well as definitive answers.

15:15 - 16:10    Cairnes Lecture Theatre

Richard Haydon (University of Oxford):
On the scalar-plus-compact problem

A problem that has been open for some time is whether there exists a Banach space on which every bounded linear operator has the form \lambda I + K with \lambda a scalar and K a compact operator. The talk will discuss the background to the problem, and its recent solution by S.A. Argyros and the speaker.