Ondřej Kurka

Tsirelson-like spaces and complexity of classes of Banach spaces

Employing a construction of Tsirelson-like spaces due to Argyros and Deliyanni, we show that the class of all Banach spaces which are isomorphic to a subspace of

Reflexivity and sets of Fréchet subdifferentiability

c_{0}

Non-universal families of separable Banach spaces

c0 is a complete analytic set with respect to the Effros Borel structure of separable Banach spaces. Moreover, the classes of all separable spaces with the Schur property and of all separable spaces with the Dunford–Pettis property are

Genericity of Fréchet smooth spaces

\Pi ^{1}_{2}

Large separated sets of unit vectors in Banach spaces of continuous functions

Π21-complete.

On Borel classes of sets of Frechet subdifferentiability

It was proved by Argyros and Dodos that, for many classes