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.
