<p>It is shown that the constant <i>c</i><sub><i>d</i>,3</sub> in von Neumann’s inequality for <i>d</i>-tuples of commutative and row contractive 3 × 3 matrices, as proved by Hartz, Richter, and Shalit in [2], is independent of the size of the <i>d</i>-tuple. A numerical estimation of the constant is provided.</p>

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The von Neumann inequality for 3 × 3 matrices in the unit Euclidean ball

  • Dariusz Piekarz

摘要

It is shown that the constant cd,3 in von Neumann’s inequality for d-tuples of commutative and row contractive 3 × 3 matrices, as proved by Hartz, Richter, and Shalit in [2], is independent of the size of the d-tuple. A numerical estimation of the constant is provided.