Ultraproducts of crossed product C * algebras

Abstract We study the relationship between the ultraproduct of a crossed product C * algebra ( A ⋊ r G ) ω ${(\mathcal {A}\rtimes _{r}G)^{\omega }}$ left parenthesis script upper A right normal factor semidirect product Subscript r Baseline upper G right parenthesis Superscript omega and the crossed product of an ultraproduct C * algebra A ω ⋊ r G $\mathcal {A}^{\omega }\rtimes _{r}G$ script upper A Superscript omega Baseline right normal factor semidirect product Subscript r Baseline upper G for a fixed free ultrafilter ω $\omega $ omega on N $\mathbb {N}$ double struck upper N . For a general locally compact amenable group G , we show that A α ω ⋊ r G $\mathcal {A}^{\omega }_{\alpha }\rtimes _{r}G$ script upper A Subscript alpha Superscript omega Baseline right normal factor semidirect product Subscript r Baseline upper G embeds into ( A ⋊ r G ) ω $(\mathcal {A}\rtimes _{r}G)^{\omega }$ left parenthesis script upper A right normal factor