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Published 2001 | public
Journal Article

Existence of Non-Trivial Bounded Functionals Implies the Hahn-Banach Extension Theorem


We show that it is impossible to prove the existence of a linear (bounded or unbounded) functional on any L_∞/C_0 without an uncountable form of the axiom of choice. Moreover, we show that if on each Banach space there exists at least one non-trivial bounded linear functional, then the Hahn-Banach extension theorem must hold. We also discuss relations of non-measurable sets and the Hahn-Banach extension theorem.

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© 2001 EMS Publishing House.

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August 19, 2023
October 18, 2023