The existence of non-trivial bounded functionals implies the Hahn-Banach extension theorem

Citation
Waj. Luxemburg et M. Vath, The existence of non-trivial bounded functionals implies the Hahn-Banach extension theorem, Z ANAL ANWE, 20(2), 2001, pp. 267-279
Citations number
51
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN
ISSN journal
0232-2064 → ACNP
Volume
20
Issue
2
Year of publication
2001
Pages
267 - 279
Database
ISI
SICI code
0232-2064(2001)20:2<267:TEONBF>2.0.ZU;2-L
Abstract
We show that it is impossible to prove the existence of a linear (bounded o r unbounded) functional on any L-infinity/C-o without an uncountable form o ft he axiom of choice. Moreover., we show that if on each Banach space ther e exists at least one non-trivial bounded linear functional, then the Hahn- Banach extension theorem must hold. We also discuss relations of non-measur able sets and the Hahn-Banach extension theorem.