Given a -dynamical system , it is well-known that the -vector space of compactly-supported continuous functions from to can be equipped with a convolution operation and an involution operation . In order to form the crossed-product -algebra associated to , one then completes with respect to the universal norm coming from all contractive -homomorphisms from to a -algebra, where contractivity is with respect to the -norm on , for a given Haar measure on . One can then ask: Is contractivity obtainable for free for any -homomorphism from to a -algebra? No counterexamples are currently known, and hardly anything in the literature has been written related to this question. In this talk, I will start the ball rolling by proving for any discrete twisted -dynamical system that a -homomorphism from to a -algebra is automatically contractive with respect to the -norm on — for any positive-scalar multiple of the counting measure on .
Automatic Continuity of *-Representations for Discrete Twisted -Dynamical Systems