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Quantized convolution semigroups
We describe our construction of a continuous tensor product system in the sense of Arveson for a general W * -continuous completely positive semigroup of B(H) (H separable). This product system is canonically isomorphic to the product system of the minimal dilation E 0 -semigroup. We use this construction to show that contrary to previous speculation the minimal dilations of all quantized convolution semigroups are completely spatial. This class includes the heat flow on the CCR algebra studieddoi:10.1090/conm/335/06011 fatcat:c7leaio7hfdwtk5ruhfbyf4jzq