Dual piecewise analytic bundle shift models of linear operators (Q1911510)

Let \(T\) be a Banach space operator with empty point spectrum, whose essential spectrum lies on a finite system of (possibly intersecting) curves. Under certain conditions on \(T\), dual analytic representations of \(T\) as a kind of bundle shift and of \(T^*\) as an ``adjoint bundle shift'' are constructed. The author gives a specialization of this scheme which allows him to obtain in some cases concrete similarity models of \(T\) and \(T^*\) in certain analogues of Smirnov \(E^2\)-spaces. He applies this construction to Toeplitz operators with smooth symbols.