Operators with singular continuous spectrum: II. Rank one operators |
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| Authors: | R Del Rio N Makarov B Simon |
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| Institution: | (1) Division of Physics, Astronomy and Mathematics, California Institute of Technology, 253-37, 91125 Pasadena, CA, USA;(2) Present address: IIMAS-UNAM, Admon. No. 20, Apdo. Postal 20-726, 01000 Mexico, D.F., Mexico |
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| Abstract: | For an operator,A, with cyclic vector  , we studyA+ P, whereP is the rank one projection onto multiples of . If  , ]  spec (A) andA has no a.c. spectrum, we prove thatA+P has purely singular continuous spectrum on (,) for a denseG
 of 's.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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