On characterizations of amenable $$\hbox {C}^*$$-dynamical systems and new examples

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<jats:title>Abstract</jats:title><jats:p>We show the equivalence of several amenability type conditions for<jats:inline-formula><jats:alternatives><jats:tex-math>$$\hbox {C}^*$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>C</mml:mtext><mml:mo>∗</mml:mo></mml:msup></mml:math></jats:alternatives></jats:inline-formula>-dynamical systems. As an application, based on the Pimsner–Meyer construction, we give a new method to produce amenable actions on simple<jats:inline-formula><jats:alternatives><jats:tex-math>$$\hbox {C}^*$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>C</mml:mtext><mml:mo>∗</mml:mo></mml:msup></mml:math></jats:alternatives></jats:inline-formula>-algebras.</jats:p>

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  • Selecta Mathematica

    Selecta Mathematica 27 (5), 2021-09-20

    Springer Science and Business Media LLC

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