Dual Piecewise Analytic Bundle Shift Models of Linear Operators

LetTbe a Banach space operator with empty point spectrum, whose essential spectrum lies on a finite system of (possibly intersecting) curves. Under certain conditions onT, dual analytic representations ofTas a kind of bundle shift and of T* as an “adjoint bundle shift” are constructed. A specialization of this scheme is given, which allows one to obtain in some cases concrete similarity models ofTandT* in certain analogues of SmirnovE2-spaces. The latter construction is applied to Toeplitz operators with smooth symbols.