Finite dimensional invariant subspaces for algebras of linear operators and amenable Banach algebras

摘要

We study a finite dimensional invariant subspace property similar to Fan's Theorem on semigroups for arbitrary Banach algebras A in terms of amenability of X(A, phi), the closed subalgebra of A generated by the set of all maximal elements in A with respect to a character phi. As a consequence, we offer some applications to the measure algebra M(G) and the generalized Fourier algebra A(p)(G) of a locally compact group G. (C) 2016 Elsevier Inc. All rights reserved.