Amenability and invariant subspaces

  title={Amenability and invariant subspaces},
  author={Anthony To-ming Lau},
Let E be a topological vector space (over the real or complex field). A well-known geometric form of the Hahn-Banach theorem asserts that if U is an open convex subset of E and M is a subspace of E which does not meet U , then there exists a closed hyperplane H containing M and not meeting U . In this paper we prove, among other things, that if S is a left amenable semigroup (which is the case, for example, when S is abelian or when S is a solvable group, see [3, p.11]), then for any right… CONTINUE READING