Operators with singular continuous spectrum: II. Rank one operators (original) (raw)

1994, Communications in Mathematical Physics

Abstract

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.

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