Abstract
In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense G δ {G_\delta } .
Highlights
Our goal here is to announce results that show that a singular continuous spectrum lies quite close to many operators by proving it is often generic in the Baire sense
This material is based upon work of the third author supported by National Science Foundation grant DMS-9207071
The government has certain rights in this material. This material is based upon work of the first and fourth authors supported by National Science Foundation grant DMS-9101715
Summary
Our goal here is to announce results that show that a singular continuous spectrum lies quite close to many operators by proving it is often generic in the Baire sense. For a dense Gg of V £ CodW), -A + V has purely singular continuous spectrum on (0, oo). This material is based upon work of the third author supported by National Science Foundation grant DMS-9207071. This material is based upon work of the first and fourth authors supported by National Science Foundation grant DMS-9101715.
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