EXTREME POINT METHODS IN THE STUDY OF ISOMETRIES ON CERTAIN NONCOMMUTATIVE SPACES

Abstract In this paper, we characterize surjective isometries on certain classes of noncommutative spaces associated with semi-finite von Neumann algebras: the Lorentz $L^{w,1}$ , as well $L^1+L^\infty$ and $L^1\cap L^\infty$ . The technique used in all three cases relies characterizations extreme points unit balls these spaces. Of particular interest is that representations obtained paper are global representations.