Operators with singular continuous spectrum: II. Rank one operators
نویسندگان
چکیده
منابع مشابه
Operators with Singular Continuous Spectrum: Ii. Rank One Operators
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 Gδ of λ’s. §
متن کاملOperators with Singular Continuous Spectrum
The Baire category theorem implies that the family, F,of dense sets G6 in a fixed metric space, X , is a candidate for generic sets since it is closed under countable intersections; and if X is perfect (has no isolated point), then A E F has uncountable intersections with any open ball in X. There is a long tradition of soft arguments to prove that certain surprising sets are generic. For examp...
متن کاملOperators with Singular Continuous Spectrum: III. Almost Periodic Schrόdinger Operators
We prove that one-dimensional Schrodinger operators with even almost periodic potential have no point spectrum for a dense Gδ in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a dense Gδ in Θ even if the frequency is an irrational with good Diophantine properties.
متن کاملOperators with Singular Continuous Spectrum: I. General Operators
§0. Introduction The Baire category theorem implies that the family, F , of dense sets Gδ in a fixed metric space, X, is a candidate for generic sets since it is closed under countable intersections; and if X is perfect (has no isolated point), then A ∈ F has uncountable intersections with any open ball in X. There is a long tradition of soft arguments to prove that certain surprising sets are ...
متن کاملOperators with Singular Continuous Spectrum: Iii. Almost Periodic Schrödinger Operators
We prove that one-dimensional Schrödinger operators with even almost periodic potential have no point spectrum for a dense Gδ in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a dense Gδ in θ even if the frequency is an irrational with good Diophantine properties. §
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1994
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02099737