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Amenable Crossed Product Banach Algebras Associated with a Class of $$\varvec{{\mathrm C}^*}$$ C โ -Dynamical Systems
We prove that the crossed product Banach algebra $$\ell ^1(G,A;\alpha )$$ that is associated with a $${\mathrm C}^*$$ -dynamical system $$(A,G,\alpha )$$ is amenable if G is a discrete amenable group and A is a commutative or finite dimensional $${\mathrm C}^*$$ -algebra. Perspectives for further developments are indicated.