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Operators with singular continuous spectrum: II. Rank one operators

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/BF02099737DOIArticle
https://link.springer.com/article/10.1007%2FBF02099737PublisherArticle
http://rdcu.be/yYu2PublisherFree ReadCube access
ORCID:
AuthorORCID
Simon, B.0000-0003-2561-8539
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.
Funders:
Funding AgencyGrant Number
Universidad Nacional Autónoma de México (UNAM)UNSPECIFIED
Consejo Nacional de Ciencia y Tecnología (CONACYT)UNSPECIFIED
NSFDMS-9207071
NSFDMS-9101715
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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