Extensions of C*-dynamical systems to systems with complete transfer operators

Details Extensions of C*-dynamical systems to systems with complete transfer operators Extensions of C*-dynamical systems to systems with complete transfer operators

2007-03-27

arxiv.org/abs/math/0703800v2

Mathematics

Operator Algebras

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Scientific paper

Starting from an arbitrary endomorphism \alpha of a unital C*-algebra A we construct a bigger algebra B and extend \alpha onto B in such a way that the extended endomorphism \alpha has a unital kernel and a hereditary range, i.e. there exists a unique non-degenerate transfer operator for (\B,\alpha). The pair (\B,\alpha) is universal with respect to a suitable notion of covariant representation and thus enables a natural definition of the crossed product $\A\rtimes_\alpha \N$ for arbitrary $\alpha$.

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