Abstract
In the preceding chapters we considered µC*-algebras generated by functional operators, and for this reason the results obtained therein apply mainly to operators in spaces L2(X, µ). When we change the setting to other function spaces, the properties of functional operators change considerably. In this section we consider weighted shift operators in spaces of smooth functions on a segment and clarify the dependence of the spectral properties of operators on the parameter/that characterizes the degree of smoothness of functions.
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