Representation of Suslin sets by operators (Q1067181)

The main result is the following: Let \({\mathcal S}\) be a bounded Suslin set in the plane. There is a bounded linear operator T in E, whose point spectrum \(\sigma_ e(T)\) is \({\mathcal S}\). Furthermore the operator T can be chosen from a fixed collection that is \(\sigma\)-compact in the operator norm. In fact, the Banach space is a space of functionals on \(C^ 1_ c({\mathbb{R}})\), not dependent on \({\mathcal S}\). The operator is multiplication by a Hölder-continuous function with exponent 1/3.