# von Neumann's inequality for row contractive matrix tuples

@inproceedings{Hartz2021vonNI, title={von Neumann's inequality for row contractive matrix tuples}, author={Michael Hartz and Stefan Richter and Orr Shalit}, year={2021} }

We prove that for all n ∈ N, there exists a constant Cn such that for all d ∈ N, for every row contraction T consisting of d commuting n× n matrices and every polynomial p, the following inequality holds: ‖p(T )‖ ≤ Cn sup z∈Bd |p(z)|. We apply this result and the considerations involved in the proof to several open problems from the pertinent literature. First, we show that Gleason’s problem cannot be solved contractively in H∞(Bd) for d ≥ 2. Second, we prove that the multiplier algebra Mult(Da…

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