Abstract
Starting from an arbitrary endomorphism α of a unital C*-algebra A we construct in a canonical way a bigger algebra B and extend α onto B in such a way that α : B → B possess a unique non-degenerate transfer operator L: B → itB called complete transfer operator. The pair (B, α) is universal with respect to a suitable notion of a covariant representation and in general depends on a choice of an ideal in A.
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Kwaśniewski, B.K. Extensions of C*-dynamical systems to systems with complete transfer operators. Math Notes 98, 419–428 (2015). https://doi.org/10.1134/S0001434615090072
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DOI: https://doi.org/10.1134/S0001434615090072