The stabilized set of p's in Krivine's theorem can be disconnected |
| |
Authors: | Kevin Beanland Daniel Freeman Pavlos Motakis |
| |
Affiliation: | 1. Department of Mathematics, Washington and Lee University, Lexington, VA 24450, United States;2. Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, United States;3. National Technical University of Athens, Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, 157 80, Athens, Greece |
| |
Abstract: | For any closed subset F of [1,∞] which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space X with a 1-unconditional basis is constructed so that in each block subspace Y of X , ?p is finitely block represented in Y if and only if p∈F. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace Y of X there is a dense subset G of F such that the spreading models admitted by Y are exactly the ?p for p∈G. |
| |
Keywords: | 46B03 46B06 46B07 46B25 46B45 |
本文献已被 ScienceDirect 等数据库收录! |
|