Abstract
Starting from some classical counterexamples to the von Neumann inequality for several variables, we are led to especially simple examples of this phenomenon. We display three commuting 4-dimensional contractions Ck and a polynomial p(zi, z2, z3) such that
We find that this phenomenon depends on the norm of Schur multiplication by certain matrices and on the related Haagerup factorizations. It is easy to perturb the example to a triple of generic commuting contractions and so provide an answer to a question of Lewis and Wermer.
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Holbrook, J.A. (2001). Schur norms and the multivariate von Neumann inequality. In: Kérchy, L., Gohberg, I., Foias, C.I., Langer, H. (eds) Recent Advances in Operator Theory and Related Topics. Operator Theory: Advances and Applications, vol 127. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8374-0_20
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DOI: https://doi.org/10.1007/978-3-0348-8374-0_20
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