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Febuary 2020 On von Neumann's inequality for complex triangular Toeplitz contractions
Joachim Moussounda Mouanda
Rocky Mountain J. Math. 50(1): 213-224 (Febuary 2020). DOI: 10.1216/rmj.2020.50.213

Abstract

We prove that von Neumann’s inequality holds for circulant contractions. We show that every complex polynomial f(z1,,zn) over 𝔻n is associated to a constant d(f) such that von Neumann’s inequality can hold up to d(f), for n-tuples of commuting contractions on a Hilbert space. We characterise complex polynomials over 𝔻n in which d(f)=2. We introduce the properties of upper (or lower) complex triangular Toeplitz matrices. We show that von Neumann’s inequality holds for n-tuples of upper (or lower) complex triangular Toeplitz contractions. We construct contractive homomorphisms.

Citation

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Joachim Moussounda Mouanda. "On von Neumann's inequality for complex triangular Toeplitz contractions." Rocky Mountain J. Math. 50 (1) 213 - 224, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.213

Information

Received: 24 December 2017; Revised: 5 September 2019; Accepted: 5 September 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201563
MathSciNet: MR4092553
Digital Object Identifier: 10.1216/rmj.2020.50.213

Subjects:
Primary: 47A65, 47A68

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 1 • Febuary 2020
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