The Hahn-Banach Theorem surveyed

Gerard Buskes

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1993

Abstract

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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........................................................................................361991 Mathematics Subject Classification: Primary 46A22, 46-02; Secondary 04A25, 46M10, 46P05, 47B55.

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Gerard Buskes. The Hahn-Banach Theorem surveyed. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1993. <http://eudml.org/doc/268338>.

@book{GerardBuskes1993,
abstract = {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........................................................................................361991 Mathematics Subject Classification: Primary 46A22, 46-02; Secondary 04A25, 46M10, 46P05, 47B55.},
author = {Gerard Buskes},
keywords = {Hahn-Banach Theorem; Mazur-Orlicz theorem; simultaneous Hahn-Banach extensions; interpolation property; injective Banach spaces; injective Banach lattices; invariant extensions; Banach limits; amenability property},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {The Hahn-Banach Theorem surveyed},
url = {http://eudml.org/doc/268338},
year = {1993},
}

TY - BOOK
AU - Gerard Buskes
TI - The Hahn-Banach Theorem surveyed
PY - 1993
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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........................................................................................361991 Mathematics Subject Classification: Primary 46A22, 46-02; Secondary 04A25, 46M10, 46P05, 47B55.
LA - eng
KW - Hahn-Banach Theorem; Mazur-Orlicz theorem; simultaneous Hahn-Banach extensions; interpolation property; injective Banach spaces; injective Banach lattices; invariant extensions; Banach limits; amenability property
UR - http://eudml.org/doc/268338
ER -

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