von Neumann’s inequality for commuting, diagonalizable contractions. II
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- by B. A. Lotto and T. Steger PDF
- Proc. Amer. Math. Soc. 120 (1994), 897-901 Request permission
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 $||p(T)|| > ||p|{|_\infty }$, where $||p|{|_\infty }$ denotes the supremum norm of $p$ over the unit polydisk in ${{\mathbf {C}}^3}$.References
- John A. R. Holbrook, Polynomials in a matrix and its commutant, Linear Algebra Appl. 48 (1982), 293–301. MR 683226, DOI 10.1016/0024-3795(82)90115-X
- B. A. Lotto, von Neumann’s inequality for commuting, diagonalizable contractions. I, Proc. Amer. Math. Soc. 120 (1994), no. 3, 889–895. MR 1169881, DOI 10.1090/S0002-9939-1994-1169881-8
- N. Th. Varopoulos, On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory, J. Functional Analysis 16 (1974), 83–100. MR 0355642, DOI 10.1016/0022-1236(74)90071-8
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 897-901
- MSC: Primary 47A30; Secondary 15A60, 47B99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1169882-X
- MathSciNet review: 1169882