This is an announcement for the paper “Asymptotically symmetric spaces with hereditarily non-unique spreading models” by Denka Kutzarovahttps://arxiv.org/search/math?searchtype=author&query=Kutzarova%2C+D, Pavlos Motakishttps://arxiv.org/search/math?searchtype=author&query=Motakis%2C+P.

Abstract: We examine a variant of a Banach space $\mathfrak{X}_{0,1}$ defined by Argyros, Beanland, and the second named author that has the property that it admits precisely two spreading models in every infinite dimensional subspace. We prove that this space is asymptotically symmetric and thus it provides a negative answer to a problem of Junge, the first. named author, and Odell.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1902.10098