CONTENTS1. Prerequisites....................................................................................52. The history.......................................................................................63. Helly's Part.......................................................................................64. Banach's proof.................................................................................75. The shortest proof...........................................................................86. Luxemburg's proof.........................................................................107. Nachbin's proof..............................................................................118. Mazur's geometric Hahn-Banach Theorem....................................129. The complex numbers....................................................................1310. Ingleton's Theorem......................................................................1411. Constructive analysis and unique extensions...............................1612. The Axiom of Choice and the Ultrafilter Theorem.........................1813. The Mazur-Orlicz Theorem...........................................................2114. Simultaneous Hahn-Banach extensions.......................................2315. Injective Banach spaces and injective Banach lattices.................2416. The interpolation property............................................................2617. Invariant extensions.....................................................................2818. Locally convex spaces.................................................................2919. Non-commutative Hahn-Banach Theorems..................................3020. The strength of the Hahn-Banach Theorem.................................3121. Other categories..........................................................................32 21.1. Groups and semigroups..........................................................32 21.2. Vector lattices..........................................................................33 21.3. Algebras..................................................................................34 21.4. Distributive lattices and Boolean algebras..............................34 21.5. Module versions of the Hahn-Banach Theorem......................35References........................................................................................36
1991 Mathematics Subject Classification: Primary 46A22, 46-02; Secondary 04A25, 46M10, 46P05, 47B55.
@book{bwmeta1.element.zamlynska-68970a45-5c73-4016-b0e9-c73fc3305d2d,
author = {Gerard Buskes},
title = {The Hahn-Banach Theorem surveyed},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1993},
zbl = {0808.46003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-68970a45-5c73-4016-b0e9-c73fc3305d2d}
}
Gerard Buskes. The Hahn-Banach Theorem surveyed. GDML_Books (1993), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-68970a45-5c73-4016-b0e9-c73fc3305d2d/