Abstract
The answer to the title question is “no.” The Kaijser–Varopoulos counterexample to the three-variable von Neumann inequality shows that conservative realizations do not always exist; in this note we show that this same example can be used to prove that dissipative realizations need not exist. (This is a consequence of the particular features of this example; it need not be true of every counterexample to von Neumann’s inequality.)
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Communicated by Gadadhar Misra.
Research partially supported by NSF grant DMS 1101461.
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Jury, M.T. Does Every Contractive Analytic Function in a Polydisk have a Dissipative n-Dimensional Scattering Realization?. Complex Anal. Oper. Theory 9, 821–825 (2015). https://doi.org/10.1007/s11785-014-0362-6
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DOI: https://doi.org/10.1007/s11785-014-0362-6