Analogs of the classical inequalities from the Brunn Minkowski Theory for rotation intertwining additive maps of convex bodies are developed. We also prove analogs of inequalities from the dual Brunn Minkowski Theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary we obtain a new Brunn Mi...

In this note we prove that elementary surjective maps on triangular algebras are automatically additive. The study of elementary maps was initiated by Brešar and Šerml. Following ([1]), elementary maps are defined as follows. Definition 1. Let R and R be two rings. Suppose that M : R → R and M : R → R are two maps. Call the ordered pair (M,M) an elementary map of R×R if