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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

von Neumann's inequality for commuting, diagonalizable contractions. II


Authors: B. A. Lotto and T. Steger
Journal: Proc. Amer. Math. Soc. 120 (1994), 897-901
MSC: Primary 47A30; Secondary 15A60, 47B99
MathSciNet review: 1169882
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Abstract: We construct a triple $ T = ({T_1},{T_2},{T_3})$ of commuting, diagonalizable contractions on $ {{\mathbf{C}}^5}$ and a polynomial $ p$ in three variables for which $ \vert\vert p(T)\vert\vert > \vert\vert p\vert{\vert _\infty }$, where $ \vert\vert p\vert{\vert _\infty }$ denotes the supremum norm of $ p$ over the unit polydisk in $ {{\mathbf{C}}^3}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1169882-X
PII: S 0002-9939(1994)1169882-X
Article copyright: © Copyright 1994 American Mathematical Society