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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.

##### MSC:
 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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