Retractions and the bounded approximation property in Banach spaces

Abstract

In the present paper we prove that a necessary condition for a Banach space $X$ to admit a generating compact Lipschitz retract $K$, which satisfies an additional mild assumption on its shape, is that $X$ enjoys the Bounded Approximation Property. This is a partial solution to a question raised by Godefroy and Ozawa.

arXiv admin note: text overlap with arXiv:2106.00331