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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