Equivalence of regular q-unitary dilation, Brehmer positivity, and Q-unitary dilation established for q-commuting contractions with ||q||=1 via Stinespring and Naimark theorems, with von Neumann inequality in some cases.
Fuglede, A commutativity theorem for normal operators , Proc
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Theory of $q$-commuting contractions-II: Regular dilation, Brehmer's positivity and von Neumann's inequality
Equivalence of regular q-unitary dilation, Brehmer positivity, and Q-unitary dilation established for q-commuting contractions with ||q||=1 via Stinespring and Naimark theorems, with von Neumann inequality in some cases.