Riesz projections and corona data for restricted shifts (Q1086810)

Let s be some specified inner function. The author studies boundedness problems for sequences of Riesz projections associated with the restricted shift operator S defined on \((sH^ 2)^{\perp}\) by \(Sf=Pzf\), where P is the orthogonal projection of \(H^ 2\) onto \((sH^ 2)^{\perp}\). The main result is stated in terms of Carleson's corona conditions. A description of the commutant of a set of bounded Riesz projections is also given. Closely related to the paper is the work of \textit{N. K. Nikol'skij} [Proc. Steklov Inst. Math. 130, 55-132 (1979; Zbl 0461.46012)] and \textit{V. I. Vasyunin} [ibid. 130, 1-53 (1979; Zbl 0438.47039)].