We show that the standard approach of minimal invariant sets, which applies Zorn’s Lemma and is used to prove fixed point theorems for nonexpansive mappings in Banach spaces, can be applied without any reference to the full Axiom of Choice when the given Banach space is separable. Our method applies results from classical and effective descriptive set theory.
Choice free fixed point property in separable Banach spaces
GREGORIADES, VASSILIOS
2015-01-01
Abstract
We show that the standard approach of minimal invariant sets, which applies Zorn’s Lemma and is used to prove fixed point theorems for nonexpansive mappings in Banach spaces, can be applied without any reference to the full Axiom of Choice when the given Banach space is separable. Our method applies results from classical and effective descriptive set theory.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
