k-Hyponormality of multivariable weighted shifts
نویسندگان
چکیده
منابع مشابه
k-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...
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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...
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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 ...
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We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting n-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal 2-variable weighted shifts, we then fin...
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We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite tree structure associated with the underlying Hilbert space. These shifts arise naturally through weighted versions of certain representations of the Cuntz C...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2005
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2005.03.022