%0 Journal Article
%T Finie dimensional invariant subspace property and amenability for a class of Banach algebras
%A Anthony T. -M. Lau
%A Yong Zhang
%J Mathematics
%D 2014
%I arXiv
%X Motivated by a result of Ky Fan in 1965, we establish a characterization of a left amenable F-algebra (which includes the group algebra and the Fourier algebra of a locally compact group and quantum group algebras, or more generally the predual algebra of a Hopf von Neumann algebra) in terms of a finite dimensional invariant subspace property. This is done by first revealing a fixed point property for the semigroup of norm one positive linear func- tionals in the algebra. Our result answers an open question posted in Tokyo in 1993 by the first author (see [25, Problem 5]). We also show that the left amenability of an ideal in an F-algebra may determine the left amenability of the algebra.
%U http://arxiv.org/abs/1404.3405v1