Finite dimensional invariant subspaces for algebras of linear operators and amenable Banach algebras
Let \( A\) be a Banach algebra and \(\phi\) be a character on \( A\). The authors consider \(P_1( A, \phi)\), the set of all \(\phi\)-maximal elements of \(A\), and also representations of this semigroup on separated locally convex vector spaces. They study a finite-dimensional property in terms of amenability of the closed linear span of \(P_1( A, \phi)\). They present some applications concerning the group algebra, the measure algebra and the generalized Fourier algebra of a locally compact group.
scientific article; zbMATH DE number 6668932
scientific article