Operators with singular continuous spectrum: II. Rank one operators
For an operator, A, with cyclic vector ϕ, we study A+λP, where P is the rank one projection onto multiples of ϕ. If [α,β] ⊂ spec (A) and A has no a.c. spectrum, we prove that A+λP has purely singular continuous spectrum on (α,β) for a dense G_δ of λ's.
© 1994 Springer-Verlag. Received: 12 July 1993; in revised form October 25, 1993. Research partially supported by DGAPA-UNAM and CONACYT. This material is based upon work suported by the National Science Foundation under Grant No. DMS-9207071. The Government has certain rights in this material. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.