Been doing exercises on compactness/sequential compactness of objects in Banach spaces and some of my solutions come down to whether(adsbygoogle = window.adsbygoogle || []).push({}); holds in "every bounded sequence has a convergent subsequence"

a) arbitrary finite-dimensional Banach space

b) l^{p}, 1 <= p <= infinity

Does it?

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

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!

# Compactness/convergence in Banach spaces

Loading...

Similar Threads - Compactness convergence Banach | Date |
---|---|

A Questions about Covering maps, manifolds, compactness | Oct 26, 2017 |

I Compact Disk | Oct 3, 2017 |

I Noncompact locally compact Hausdorff continuous mapping | Sep 23, 2017 |

Convergent sequence in compact metric space | Dec 9, 2012 |

Convergent subsequences in compact spaces | Jul 15, 2011 |

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