For a real reductive dual pair the Capelli identities define a homomorphism "C" from the center of the universal enveloping algebra of the larger group to the center of the universal enveloping algebra of the smaller group. In terms of the Harish-Chandra isomorphism, this map involves a "rho-shift". We view a dual pair as a Lie supergroup and offer a construction of the homomorphism "C" based solely on the Harish-Chandra's radial component maps..

Appeared in Transactions of the AMS. 356, 1121--1154 (2003).