This is an announcement for the paper "Non-universal families of separable Banach spaces" by Ondrej Kurka.

Abstract: We prove that if $ C $ is a family of separable Banach spaces which is analytic with respect to the Effros-Borel structure and none member of $ C $ is isometrically universal for all separable Banach spaces, then there exists a separable Banach space with a monotone Schauder basis which is isometrically universal for $ C $ but still not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.

Archive classification: math.FA

Mathematics Subject Classification: 46B04, 54H05 (Primary) 46B15, 46B20, 46B25 (Secondary)

Submitted from: kurka.ondrej@seznam.cz

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1508.05059

or

http://arXiv.org/abs/1508.05059