This is an announcement for the paper "Separable elastic Banach spaces are universal" by Dale E. Alspach and Bunyamin Sari.
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 $C[0,1]$ 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 $C(K)$ 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 $C(K)$ that is realized on special reproducible bases.
Archive classification: math.FA
Mathematics Subject Classification: 46B03 (primary), 46B25 (secondary)
Remarks: 27 pages
Submitted from: alspach@math.okstate.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.03791
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