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

Abstract

Starting from an arbitrary endomorphism $\alpha$ of a unital C*-algebra $A$ we construct a bigger C*-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 $(B,\alpha )$, called the complete transfer operator. The pair $(B,\alpha )$ is universal with respect to a suitable notion of a covariant representation and depends on a choice of an ideal in $A$. The construction enables a natural definition of the crossed product for arbitrary $\alpha$.

Compressed and submitted version, 9 pages

References in corpus (2)

• Crossed products by endomorphisms and reduction of relations in relative Cuntz-Pimsner algebras
• When a C*-algebra is a coefficient algebra for a given endomorphism

Cited by in corpus (1)

• Crossed products by endomorphisms of $C_0(X)$-algebras