Schur product techniques for the subnormality of commuting 2-variable weighted shifts
نویسندگان
چکیده
منابع مشابه
Subnormality of 2-variable weighted shifts with diagonal core Subnormality of 2-variable weighted shifts with diagonal core ⋆
The Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for a pair of subnormal operators on Hilbert space to admit commuting normal extensions. Given a 2-variable weighted shift T with diagonal core, we prove that LPCS is soluble for T if and only if LPCS is soluble for some power Tm (m ∈ Z+,m ≡ (m1,m2),m1,m2 ≥ 1). We do this by first developing the bas...
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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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For a, b, c, d ≥ 0 with ad − bc > 0, we consider the unilateral weighted shift S(a, b, c, d) with weights αn := √ an+b cn+d (n ≥ 0). Using Schur product techniques, we prove that S(a, b, c, d) is always subnormal; more generally, we establish that for every p ≥ 1, all p-subshifts of S(a, b, c, d) are subnormal. As a consequence, we show that all Bergman-like weighted shifts are subnormal.
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The Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for a pair of subnormal operators on Hilbert space to admit commuting normal extensions. We study LPCS within the class of commuting 2-variable weighted shifts T ≡ (T1, T2) with subnormal components T1 and T2, acting on the Hilbert space l (Z+) with canonical orthonormal basis {e(k1,k2)}k1,k2≥0 . Th...
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We show that every multivariable contractive weighted shift dilates to a tuple of commuting unitaries, and hence satisfies von Neumann’s inequality. This answers a question of Lubin and Shields. We also exhibit a closely related 3-tuple of commuting contractions, similar to Parrott’s example, which does not dilate to a 3-tuple of commuting unitaries.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.04.013