This is an announcement for the paper “Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases” by Fernando Albiachttps://arxiv.org/search/math?searchtype=author&query=Albiac%2C+F, Jose L. Ansorenahttps://arxiv.org/search/math?searchtype=author&query=Ansorena%2C+J+L, Stephen J. Dilworthhttps://arxiv.org/search/math?searchtype=author&query=Dilworth%2C+S+J, Denka Kutzarovahttps://arxiv.org/search/math?searchtype=author&query=Kutzarova%2C+D.

Abstract: In this paper we settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non superreflexive mixed-norm sequence space. As a by-product of our work, we give applications of this result to the study of conditional Schauder bases and conditional almost greedy bases in this new class of Banach spaces.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1809.03013