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arXiv · 1508.01260

Von Neumann's inequality for commuting weighted shifts

Michael Hartz
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Abstract

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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Michael Hartz. 2015-08-06. Von Neumann's inequality for commuting weighted shifts. https://doi.org/10.1512/iumj.2017.66.6074

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