Joint Colloquium: Dales -- Multi-normed spaces and multi-Banach algebras

 Speaker: Prof.  Garth Dales (Leeds) 

Title: Multi-normed spaces and multi-Banach algebras.  

Date: Friday, 24 October 2008 Time: 2:00 pm Venue: RC-4082, The Red Centre, UNSW 

Please let me (Emma Carberry, carberry@maths.usyd.edu.au) know if you would like or can
provide transport over to the University of New South Wales.  I will leave at 12:30 PM
in order to join the Speaker for lunch before his talk.  

Abstract: 

A standard first graduate course in functional analysis will cover Banach and Hilbert
spaces, dual spaces, weak topologies, bounded linear operators on Banach spaces, and
perhaps something on Banach lattices and on Banach algebras 

I have developed a variant of this theory.  In this one replaces the norm on a Banach
space E by a sequence of norms, one on each of the spaces E^n.  This enables us to
develop new results on the following topics, among others: (1) the geometry of Banach
spaces and absolutely summing operators; (2) multi-continuous linear operators,
generalizing the regular operators on a Banach lattice; (3) a more general theory of
orthogonality in Banach spaces, and a new duality theory; (4) applications to modules
over Banach algebras, especially L^2(G) over the group algebra L^1(G) for a locally
compact group G; (5) connections with the theory of amenable groups and algebras.  

I will try to sketch some of these new theories.  

Enquiries to Emma Carberry,carberry@maths.usyd.edu.au
http://www.maths.unsw.edu.au/pure/jointcolloquium.html 

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