Multi-Banach spaces and Multi-Banach Algebras

  • Date: 11/29/2007

Garth Dales (Leeds University)


University of Alberta


The very extensive theories of Banach spaces and Banach algebras,
including algebras of operators on Banach spaces, are the foundation
stones of much modern analysis.

For certain reasons M. Polyakov and I were led to introduce a more
general notion: that of a multi-Banach space. Roughly we replace a norm
on a Banach space E by a sequence of norms on the spaces E^n. Similarly
we obtain multi-Banach algebras.

I hope to convince you that this is a useful notion by showing the
following: multi-norms give information that distinguishes Banach
spaces in an apparently new way; there are lots of examples, especially
related to Banach lattices; we generate new examples of algebras of
operators on a Banach space; we capture some notions of amenability in
a new way.

Other Information: 

PIMS Distinguished Lecture 2007