Abstract:We show the existence of Lipschitz approximable separable spaces which fail Grothendieck's approximation property. This follows from the observation that any separable space with the metric compact approximation property is Lipschitz approximable. Some related results are spelled out.
Keywords: compact approximation property; Lipschitz map; Lipschitz-free Banach space
DOI: DOI 10.14712/1213-7243.2020.021
AMS Subject Classification: 47A15 46B20