Abstract
Let A be a weak-*Dirichlet algebra of L°°(m). For 0 a closed subspace M of L(m) is called invariant if feM and ge A imply that fgeM. Let B°° be a weak-*closed subalgebra of L°°(m) which contains A such that B°°MQ M for an invariant subspace M. The main result of this paper is a characterization of the left continuous invariant subspaces for B°°, which is a natural generalization of simply invariant subspaces. Applying this result with B°° = H°°(m) (or B°° = L°°(m)), the simply (or doubly) invariant subspace theorem follows. Moreover this result characterizes also the invariant subspaces which are neither simply nor doubly invariant. Merrill and Lai characterized some special invariant subspaces of this kind.
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