By Dale E. Alspach, Bünyamin Sarı
http://www.sciencedirect.com/science/article/pii/S0022123615004164
A Banach house X is elastic if there's a consistent ok in order that each time a Banach area Y embeds into X, then there's an embedding of Y into X with consistent ok . We end up that C[0,1] embeds into separable limitless dimensional elastic Banach areas, and for that reason they're common for all separable Banach areas. This confirms a conjecture of Johnson and Odell. The facts makes use of incremental embeddings into X of C(K) areas for countable compact ok of accelerating complexity. to accomplish this we strengthen a generalization of Bourgain's foundation index that applies to unconditional sums of Banach areas and turn out a strengthening of the susceptible injectivity estate of those C(K) that's discovered on distinct reproducible bases.
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Additional resources for Separable elastic Banach spaces are universal
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