I'm trying to understand the Hahn Banach theorem, that every bounded linear functional f on some subspace M of a normed linear space X can be extended to a linear functional F on all of X with the same norm, and which agrees with f on M. But the proof is non-constructive, using zorn's lemma.(adsbygoogle = window.adsbygoogle || []).push({});

So I'm trying to come up with examples so I can understand it better. For example, let L be the space of all bounded infinite sequences with the sup norm, and let M be the subspace of L consisting of those sequences that converge to some finite limit. Then, on this subspace, the functional given by taking the limit of a sequence is clearly linear and bounded. So it must extend to a bounded linear functional on all of L. But I can't imagine what such a functional would look like. Is it possible to explicitly construct one?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hahn Banach theorem example

Loading...

Similar Threads - Hahn Banach theorem | Date |
---|---|

B Some help understanding integrals and calculus in general | May 22, 2017 |

Embedding L1 in the Banach space of complex Borel measures | Jun 11, 2012 |

Prove that a normed space is not Banach | Feb 16, 2012 |

Is it possible for a Banach Space to be isomorphic to its double dual | May 9, 2008 |

Differentiation on banach spaces | Aug 13, 2006 |

**Physics Forums - The Fusion of Science and Community**