Type: Seminar

Distribution: World

Expiry: 24 Oct 2008

Auth: carberry(.pmstaff;1014.2002)@p609.pc.maths.usyd.edu.au

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 ___________________________________________________________