Exposed and strongly exposed points in symmetric spaces of measurable operators

We investigate the relationships between exposed or strongly exposed points of the unit ball of an order continuous symmetric function space E, and of the unit ball of the space of τ-measurable operators E(M, τ) associated to a semifinite von Neumann algebra (M,τ). We prove that an operator x is an exposed or strongly exposed point of the unit ball of the symmetric space of measurable operators E(M, τ) if and only if its singular value function μ(x) is an exposed or strongly exposed point of the unit ball in E, respectively. © 2013 University of Houston