We obtain the partial-wave unitarity constraints on dimension-six operators stemming from the analyses of vector boson and Higgs scattering processes as well as the inelastic scattering of standard model fermions into electroweak gauge bosons. We take into account all coupled channels, all possible helicity amplitudes, and explore a six-dimensional parameter space of anomalous couplings. Our analysis shows that for those operators affecting the Higgs couplings, present 90% confidence level constraints from global data analysis of Higgs and electroweak data are such that unitarity is not violated if $sqrt{s}leq 3.2;{rm TeV}$. For the purely gauge-boson operator $O_{WWW}$, the present bounds from triple-gauge boson analysis indicate that within its presently allowed 90% confidence level range unitarity can be violated in $fbar f to V V$ at center-of-mass energy $sqrt{s}geq 2.4;{rm TeV}$.
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