Some open problems in Banach space theory
The weak distance between Banach spaces with a symmetric basis.
A new proof of Fréchet differentiability of Lipschitz functions
We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the closure of the set of its points of Gâteaux differentiability is norm separable.
The Poulsen simplex
It is proved that there is a unique metrizable simplex whose extreme points are dense. This simplex is homogeneous in the sense that for every 2 affinely homeomorphic faces and there is an automorphism of which maps onto . Every metrizable simplex is affinely homeomorphic to a face of . The set of extreme points of is homeomorphic to the Hilbert space . The matrices which represent are characterized.
Fréchet differentiability of Lipschitz functions via a variational principle
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