Finite dimensional invariant subspaces for algebras of linear operators and amenable Banach algebras - Nasr-Isfahani, Rasoul; Nemati, Mehdi; Shahmoradi, Somayeh (Linear algebra and its applications, 2016)
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,ϕ), the closed subalgebra of A generated by the set of all maximal elements in A with respect to a character ϕ. As a consequence, we offer some applications to the measure algebra M(G) and the generalized Fourier algebra Ap(G) of a locally compact group G.