Algebras generated by a weighted shift (Q1068346)

Let T be an injective, unilateral weighted shift operator with \(\| T\| =r(T)\) and let \({\mathcal A}(T)_*\) denote the dual of the weak* closed algebra \({\mathcal A}(T)\) generated by T and I. The author proves that for each \(L\in {\mathcal A}(T)_*\), there exist vectors x,y such that \(L(A)=<Ax,y>\), for \(A\in {\mathcal A}(T)\). For a general subnormal operator T, the analogous result was proved by \textit{R. F. Olin} and \textit{J. E. Thomson} [J. Funct. Anal. 37, 271-301 (1980; Zbl 0435.47034)]. The author makes use of the techniques of Olin and Thomson and of \textit{B. C. Chevreau}, \textit{C. Pearcy} and \textit{A. L. Shields} [J. Oper. Theory 6, 375-405 (1981; Zbl 0525.47004)].