Del Rio, R. and Makarov, N. and Simon, B. (1994) Operators with singular continuous spectrum: II. Rank one operators. Communications in Mathematical Physics, 165 (1). pp. 59-67. ISSN 0010-3616. https://resolver.caltech.edu/CaltechAUTHORS:20171120-161021287
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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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| Additional Information: | © 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. | ||||||||||||
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| Issue or Number: | 1 | ||||||||||||
| Record Number: | CaltechAUTHORS:20171120-161021287 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171120-161021287 | ||||||||||||
| Official Citation: | Del Rio, R., Makarov, N. & Simon, B. Commun. Math. Phys. (1994) 165: 59. https://doi.org/10.1007/BF02099737 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 83373 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 21 Nov 2017 00:20 | ||||||||||||
| Last Modified: | 03 Oct 2019 19:05 |
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