EXISTENCE OF INVARIANT SUBSPACE FOR CERTAIN COMMUTATIVE BANACH ALGEBRAS OF OPERATORS

Abstract

The main result presented in this paper is the existence of a nontrivial subspace of an $\mathcal{A}$-module Banach space $X$ hyperinvariant for the commutative algebra $\mathcal{A}$. From this result we can deduce the 1952 theorem of J. Wermer [8] and some other classical results on the existence of a nontrivial invariant subspace.