|
Organizers |
Decomposability of von Neumann algebras associated with locally compact groups
by
Matthias Neufang
Carleton University, Ottawa, Ontario, Canada
Coauthors: Zhiguo Hu (University of Windsor)
The decomposability number of a von Neumann algebra M, denoted by dec(M), is defined to be the greatest cardinality of a family of pairwise orthogonal, non-zero projections in M. This is a very natural invariant since a von Neumann algebra is determined by its projections.
In this talk, I shall focus on those von Neumann algebras whose preduals are function spaces/Banach algebras on a locally compact group G, such as the group algebra L1(G), the measure algebra M(G), the Fourier algebra A(G), etc. I will show that, for these von Neumann algebras, the exact value of dec(M) can be expressed in terms of two dual cardinal invariants of the underlying group G; the compact covering number k(G) and the least cardinality b(G) of an open basis at the identity of G.
It turns out that the decomposability number reveals intriguing links between topology, harmonic analysis and Banach algebra theory. I shall present applications reaching from semigroup compactifications over the topological center problem to Kac algebras. Furthermore, I shall discuss in more detail the intimate relation between decomposability and Mazur's property and property (X) of higher cardinal level; here, measurable cardinals play a crucial role.
This is joint work with Zhiguo Hu.
Date received: June 18, 2003
Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calv-03.