Arbitrarily distortable Banach spaces of higher order

作者：Beanland Kevin^*; Causey Ryan; Motakis Pavlos

来源：Israel Journal of Mathematics, 2016, 214(2): 553-581.

DOI：10.1007/s11856-016-1347-0

We study an ordinal rank on the class of Banach spaces with bases that quantifies the distortion of the norm of a given Banach space. The rank AD(aEuro cent), introduced by P. Dodos, uses the transfinite Schreier families and has the property that AD(X) < omega(1) if and only if X is arbitrarily distortable. We prove several properties of this rank as well as some new results concerning higher order l (1) spreading models. We also compute this rank for several Banach spaces. In particular, it is shown that the class of Banach spaces , which each admit l (1) and c (0) spreading models hereditarily, and were introduced by S. A. Argyros, the first and third author, satisfy . This answers some questions of Dodos.

• 出版日期2016-7