Retractions and the bounded approximation property in Banach spaces

DOI10.1007/S00009-023-02270-ZarXiv2202.08085MaRDI QIDQ6391301

Petr Hájek, R. Medina

Publication date: 16 February 2022

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.

Mathematics Subject Classification ID

Spaces of operators; tensor products; approximation properties (46B28) Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (54C55) Nonlinear classification of Banach spaces; nonlinear quotients (46B80)

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