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Extreme points of the closed unit ball in C*-algebras

Rainer Berntzen (1997)

Colloquium Mathematicae

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.

Extreme points of the complex binary trilinear ball

Fernando Cobos, Thomas Kühn, Jaak Peetre (2000)

Studia Mathematica

We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space 2 . This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space 2 . As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.

Extreme topological measures

S. V. Butler (2006)

Fundamenta Mathematicae

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.

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