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

DOI10.4171/ZAA/1015zbMath0995.46007MaRDI QIDQ5945526

Martin Väth, Wilhelmus A. J. Luxemburg

Publication date: 15 October 2002

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

zbMATH Keywords

axiom of choiceaxiom of dependent choicesHahn-Banach extension theoremnon-measurable setspower of Hahn-Banach theoremShelah's model

Mathematics Subject Classification ID

Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Consistency and independence results (03E35) Other set-theoretic hypotheses and axioms (03E65) Constructive functional analysis (46S30) Axiom of choice and related propositions (03E25)

Related Items (6)

Principles of functional analysis in scales of spaces: Hahn-Banach theorem, Banach theorem on homomorphisms, and theorems on open mappings and closed graphs ⋮ Compactness of linear integral operators in ideal spaces of vector functions ⋮ On the spectrum of orthomorphisms and Barbashin operators ⋮ Countable choice and compactness ⋮ Compactness estimates for integral operators of vector functions with nonmeasurable kernels ⋮ James sequences and Dependent Choices

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