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Coarse Non-Universality of Separable Dual Banach Spaces
A functional-analysis study of the obstructions to coarse universality in separable dual Banach spaces. It proves coarse non-universality for several classes of dual spaces — those with conditional spreading bases, generalized James and James tree spaces, and quasi-reflexive spaces — and gives quantitative counterparts distinguishing coarse non-universality from the non-equi-coarse embeddings of the Kalton graphs. The distinctive tool is a Ramsey ultrafilter: although such ultrafilters usually require the Continuum Hypothesis, an absoluteness argument shows the theorems hold in ZFC alone. The techniques also recover several previously known results.