Banach spaces without minimal subspaces |
| |
Authors: | Valentin Ferenczi |
| |
Institution: | a Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, 05311-970 São Paulo, SP, Brazil b Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 851 S. Morgan Street, Chicago, IL 60607-7045, USA |
| |
Abstract: | We prove three new dichotomies for Banach spaces à la W.T. Gowers' dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers' program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size ℵ1 into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. |
| |
Keywords: | Minimal Banach spaces Dichotomies Classification of Banach spaces |
本文献已被 ScienceDirect 等数据库收录! |
|