Vol. 30, No. 2, 1969

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Characterization of certain invariant subspaces of Hp and Lp spaces derived from logmodular algebras

Samuel Merrill and Nand Lal

Vol. 30 (1969), No. 2, 463–474

Let A = A(X) be a logmodular algebra and m a representing measure on X associated with a nontrivial Gleason part. For 1 p , let Hp(dm) denote the closure of A in Lp(dm) ( w closure for p = ). A closed subspace M of Hp(dm) or Lp(dm) is called invariant if f M and g A imply that fg M. The main result of this paper is a characterization of the invariant subspaces which satisfy a weaker hypothesis than that required in the usual form of the generalized Beurling theorem, as given by Hoffman or Srinivasan.

Mathematical Subject Classification
Primary: 46.55
Received: 4 October 1968
Published: 1 August 1969
Samuel Merrill
Nand Lal