Completely Compact Herz–Schur Multipliers of Dynamical Systems

Abstract We prove that if G is a discrete group and $$(A,G,\alpha )$$ ( A , G α ) C*-dynamical system such the reduced crossed product $$A\rtimes _{r,\alpha } G$$ ⋊ r possesses property (SOAP) then every completely compact Herz–Schur -multiplier can be approximated in bounded norm by -multipliers of finite rank. As consequence, has approximation (AP) multipliers A ( ) coincide with closure multiplier norm. study class invariant provide description this case irrational rotation algebra.