Vol. 69, No. 1, 1977

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Invariant subspaces of weak-Dirichlet algebras

Takahiko Nakazi

Vol. 69 (1977), No. 1, 151–167

Let A be a weak-*Dirichlet algebra of L(m). For 0 < p , a closed subspace M of Lp(m) is called invariant if f M and g A imply that fg M. Let B be a weak-*closed subalgebra of L(m) which contains A such that BM 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 Lal characterized some special invariant subspaces of this kind. title

Mathematical Subject Classification 2000
Primary: 46J10
Received: 23 September 1975
Published: 1 March 1977
Takahiko Nakazi
Hokusei Gakuen University
2-3-1, Ohyachi-Nishi
Atsubetsu-ku Sapporo 004-8631