# Banach space theory (12w5019)

## Organizers

Steve Dilworth (University of South Carolina)

Edward Odell (The University of Texas at Austin)

(University of North Texas)

## Description

The Banff International Research Station will host the "Banach space theory" workshop from March 4th to March 9th, 2012.

From the very beginning of Functional Analysis, the general objective of the theory of infinite-dimensional Banach spaces have been mainly to establish a nice structure theory for Banach spaces. The underlying assumption was that the geometry of a Banach space must have a lot of symmetries and therefore one can find nice' substructures in it. However, there has been a fundamental shift in our understanding of infinite-dimensional phenomena starting with the discovery of structureless' (counter)-examples of Gowers and Maurey in the nineties. The new geometric phenomena exhibited by these examples were proved to be prevalent rather than being a few pathological examples. Very recently, Argyros and Haydon discovered an ultimate example; a space which admits no non-trivial' bounded linear operator. This solves a number of central problems in Functional Analysis. It is the first example of a space on which bounded linear operators are scalar plus compact'; have Invariant Subspaces'; and form an amenable Banach algebra'. The workshop brings together the leading experts to dissect the remarkable recent progress and discuss the future directions in Banach space theory.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).