Seminar on Banach and Metric Space Geometry

Date: March 31, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Andrew Swift, Texas A&M Univeristy

Title: Coarse embeddings into superstable spaces

Abstract: If a Banach space coarsely embeds into a superstable Banach space, then it must contain a basic sequence with an ℓp spreading model for some p∈[1,∞). This is a coarse analogue to a result of Y. Raynaud, which says that if a Banach space uniformly embeds into a superstable Banach space, then it must contain a subspace isomorphic to ℓp for some p∈[1,∞). The result obtained implies that not every reflexive Banach space is coarsely embeddable into a superstable Banach space. A sketch of the proof will be given, and comparisons to Raynaud's proof in the uniform case will be made. This is joint work with B. M. Braga.