Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589719 | Journal of Functional Analysis | 2016 | 24 Pages |
Abstract
A Banach space X is elastic if there is a constant K so that whenever a Banach space Y embeds into X, then there is an embedding of Y into X with constant K . We prove that C[0,1]C[0,1] embeds into separable infinite dimensional elastic Banach spaces, and therefore they are universal for all separable Banach spaces. This confirms a conjecture of Johnson and Odell. The proof uses incremental embeddings into X of C(K)C(K) spaces for countable compact K of increasing complexity. To achieve this we develop a generalization of Bourgain's basis index that applies to unconditional sums of Banach spaces and prove a strengthening of the weak injectivity property of these C(K)C(K) that is realized on special reproducible bases.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dale E. Alspach, Bünyamin Sarı,