A generalization of von Neumann’s inequality to the complex ball

Drury, S. W.

doi:10.1090/S0002-9939-1978-0480362-8

A generalization of von Neumann’s inequality to the complex ball
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by S. W. Drury

Proc. Amer. Math. Soc. 68 (1978), 300-304

DOI: https://doi.org/10.1090/S0002-9939-1978-0480362-8

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Abstract:

A necessary and sufficient condition is found for a polynomial Q of J variables to be such that $Q({A_1}, \ldots ,{A_J})$ is a contraction whenever ${A_j}(1 \leqslant j \leqslant J)$ are commuting linear operators on complex hilbert space satisfying $\Sigma _{j = 1}^JA_j^ \ast {A_j} \leqslant I$.

References

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