Extreme points and rotundity in Musielak-Orlicz-Bochner function spaces endowed with Orlicz norm.
We investigate which points in the unit sphere of the Besicovitch--Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.
In this short note we give a short and elementary proof of a characterization of those extreme points of the closed unit ball in C*-algebras which are unitary. The result was originally proved by G. K. Pedersen using some methods from the theory of approximation by invertible elements.
We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space . This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space . As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.
It has been an open question since 1997 whether, and under what assumptions on the underlying space, extreme topological measures are dense in the set of all topological measures on the space. The present paper answers this question. The main result implies that extreme topological measures are dense on a variety of spaces, including spheres, balls and projective planes.