Commuting unilateral shifts
نویسندگان
چکیده
منابع مشابه
Von Neumann’s Inequality for Commuting Weighted Shifts
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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Let E be a star-shaped Banach space of analytic functions on the open unit disk D. It is assumed that the unilateral shift S : z → zf and the backward shift T : f → f−f(0) z are bounded on E and that their spectrum is the closed unit disk. Let M be a closed z-invariant subspace of E such that dim(M/zM) = 1, and let g ∈ M . The main result of the paper states that if g has an analytic extension ...
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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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1970-0265958-3