$k$-hyponormality of finite rank perturbations of unilateral weighted shifts
نویسندگان
چکیده
منابع مشابه
k-HYPONORMALITY OF FINITE RANK PERTURBATIONS OF UNILATERAL WEIGHTED SHIFTS
Abstract. In this paper we explore finite rank perturbations of unilateral weighted shifts Wα. First, we prove that the subnormality of Wα is never stable under nonzero finite rank pertrubations unless the perturbation occurs at the zeroth weight. Second, we establish that 2-hyponormality implies positive quadratic hyponormality, in the sense that the Maclaurin coefficients ofDn(s) := detPn [(W...
متن کاملk-HYPONORMALITY OF MULTIVARIABLE WEIGHTED SHIFTS
We characterize joint k-hyponormality for 2-variable weighted shifts. Using this characterization we construct a family of examples which establishes and illustrates the gap between k-hyponormality and (k+1)-hyponormality for each k ≥ 1. As a consequence, we obtain an abstract solution to the Lifting Problem for Commuting Subnormals. 1. Notation and Preliminaries The Lifting Problem for Commuti...
متن کاملk-HYPONORMALITY OF POWERS OF WEIGHTED SHIFTS VIA SCHUR PRODUCTS
Let H be a separable, infinite dimensional complex Hilbert space and let B(H) be the algebra of bounded linear operators on H. An operator T∈ B(H) is said to be normal if T ∗T = TT ∗, subnormal if T is the restriction of a normal operator (acting on a Hilbert space K ⊇ H) to an invariant subspace, and hyponormal if T ∗T ≥ TT ∗. The Bram-Halmos criterion for subnormality states that an operator ...
متن کاملPerturbations of Multidimensional Shifts of Finite Type
In this paper, we study perturbations of multidimensional shifts of finite type. Specifically, for any Z shift of finite type X with d > 1 and any finite pattern w in the language of X, we denote by Xw the set of elements of X not containing w. For strongly irreducible X and patterns w with shape a d-dimensional cube, we obtain upper and lower bounds on h(X) − h(Xw) dependent on the size of w. ...
متن کاملFinite Rank Perturbations and Distribution Theory
Perturbations AT of a selfadjoint operator A by symmetric finite rank operators T from H2(A) to H−2(A) are studied. The finite dimensional family of selfadjoint extensions determined by AT is given explicitly.
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: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-05-04029-8