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Dual piecewise analytic bundle shift models of linear operators. (English) Zbl 0867.47010
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.

47A45 Canonical models for contractions and nonselfadjoint linear operators
47A65 Structure theory of linear operators
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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