A generalised Green-Julg theorem for proper groupoids and Banach algebras
Abstract
The Green-Julg theorem states that K0G(B) is isomorphic to K0(L1(G,B)) for every compact group G and every G-C*-algebra B. We formulate a generalisation of this result to proper groupoids and Banach algebras and deduce that the Bost assembly map is surjective for proper Banach algebras. On the way, we show that the spectral radius of an element in a C0(X)-Banach algebra can be calculated from the spectral radius in the fibres.
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