arXiv subjects

N. de Rancourt

Publications and source records attributed to N. de Rancourt.

4 recordsLinked to original sources

arXiv2021

Local Banach-space dichotomies and ergodic spaces

We prove a local version of Gowers' Ramsey-type theorem [Ann. Math. 156 (2002)], as well as local versions both of the Banach space first dichotomy (the "unconditional/HI" dichotomy) of Gowers [Ann. Math. 156 (2002)] and of the third dichotomy (the "minimal/tight" dichotomy) due to Ferenczi-Rosendal [J. Funct. Anal. 257 (2009)]. This means that we obtain versions of these dichotomies restricted to certain families of subspaces called D-families, of which several concrete examples are given. As a main example, non-Hilbertian spaces form D-families; therefore versions of the above properties for non-Hilbertian spaces appear in new Banach space dichotomies. As a consequence we obtain new information on the number of subspaces of non-Hilbertian Banach spaces, making some progress towards the "ergodic" conjecture of Ferenczi-Rosendal and towards a question of Johnson.

math.FA↗

arXiv2021

The Feldman-Moore, Glimm-Effros, and Lusin-Novikov theorems over quotients

We establish generalizations of the Feldman-Moore theorem, the Glimm-Effros dichotomy, and the Lusin-Novikov uniformization theorem from Polish spaces to their quotients by Borel orbit equivalence relations.

math.LO↗

arXiv2021

A dichotomy for countable unions of smooth Borel equivalence relations

We show that if an equivalence relation $E$ on a Polish space is a countable union of smooth Borel subequivalence relations, then there is either a Borel reduction of $E$ to a countable Borel equivalence relation on a Polish space or a continuous embedding of $\mathbb{E}_1$ into $E$. We also establish related results concerning countable unions of more general Borel equivalence relations.

math.LO↗

arXiv2020

Connected components of the general linear group of a real hereditarily indecomposable Banach space

We give a complete description of the structure of the connected components of the general linear group of a real hereditarily indecomposable Banach space, depending on the existence of complex structures on the space itself and on its hyperplanes. A side result is the fact that complex structures cannot exist simultaneously on such a space and on its hyperplanes.

math.FA↗