Orbits in fully symmetric spaces

Abstract: 

Semigroup of simultaneous contractions in L1 and L∞ is considered. In this talk we provide a criterion for the orbit of a particular element with respect to this semigroup to coincide with the closed convex hull of its extreme points. Sufficient condition was given by Braverman and Mekler more than 30 years ago. Some examples and applications are also given.