The Rokhlin property for endomorphisms and strongly self-absorbing $C^{*}$-algebras

Abstract

In this paper, we define a Rokhlin property for automorphisms of non-unital $C^{*}$-algebras and for endomorphisms. We show that the crossed product of a $C^{*}$-algebra by a Rokhlin automorphism preserves absorption of a strongly self-absorbing $C^{*}$-algebra, and use this result to deduce that the same result holds for crossed products by endomorphisms in the sense of Stacey. This generalizes earlier results of the second named author and W. Winter.