Vol. 70, No. 2, 1977

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Sums of invariant subspaces

David A. Stegenga

Vol. 70 (1977), No. 2, 567–584

This paper is concerned with certain functional analytic and functional theoretic questions concerning the spaces of bounded analytic and bounded harmonic functions in the unit disk.

Specifically, a characterization is given of those weak-star closed, invariant subspaces of L, on the unit circle, whose vector space sum with the space of continuous function is uniformly closed. This generalizes Sarason‘s result that H + C is a closed subspace. The characterization involves the notion of local distances to H. In addition, a partial solution is given to a problem raised by Sarason concerning the structure of functions in H + C.

Mathematical Subject Classification 2000
Primary: 46J15
Received: 20 September 1976
Revised: 23 March 1977
Published: 1 June 1977
David A. Stegenga