  Rotation intertwining maps from the set of convex bodies in Rn into itself
that are continuous linear operators with respect to Minkowski and Blaschke
addition are investigated. The main focus is on Blaschke-Minkowski
homomorphisms. We show that such maps are represented by a spherical
convolution operator. An application of this representation is a complete
classification of all even Blaschke-Minkowski homomorphisms which shows that
these maps behave in many respects similar to the well known projection body
operator. Among further applications is the following result: If an even
Blaschke-Minkowski homomorphism maps a convex body to a polytope, then it is a
constant multiple of the projection body operator.
