11/07/2008, 15:15 — 16:00 — Room P3.10, Mathematics Building
Matthew Heath, Instituto Superior Técnico, U.T. Lisboa
Compact failure of multiplicativity for linear maps between Banach
algebras
The definition of compactness (and that of weak compactness) for
a linear map between normed spaces may be extended to multilinear
maps in a fairly natural way. We treat compactness as a sort of
"smallness" condition for multilinear maps. For Banach algebras
and we call a linear map, , a
cf-homomorphism (meaning "compact from a homomorphism") if the
bilinear map , (i.e. if the "failure to be multiplicative") is a compact
bilinear map. We give general theorems showing that such maps are
rather well behaved as well as numerous examples. In particular we
characterise the pairs of compact, Hausdorff spaces and for
which cf-isomorphisms from to are automatically
multiplicative.