OPERATORS WITH SINGULAR CONTINUOUS-SPECTRUM .2. RANK-ONE OPERATORS

Authors
DELRIO R MAKAROV N SIMON B
Citation
R. Delrio et al., OPERATORS WITH SINGULAR CONTINUOUS-SPECTRUM .2. RANK-ONE OPERATORS, Communications in Mathematical Physics, 165(1), 1994, pp. 59-67
Citations number
14
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
165
Issue
1
Year of publication
1994
Pages
59 - 67
Database
ISI
SICI code
0010-3616(1994)165:1<59:OWSC.R>2.0.ZU;2-5
Abstract
For an operator, A, with cyclic vector phi, we study A + lambdaP, wher e P is the rank one projection onto multiples of phi. If [alpha, beta] subset-of spec(A) and A has no a.c. spectrum, we prove that A + lambd aP has purely singular continuous spectrum on (alpha, beta) for a dens e G(delta) of lambda's.