Prove that if a Banach space X, has separable dual X*, then X is separable.(adsbygoogle = window.adsbygoogle || []).push({});

It gives the hint that the first line of the proof should be to take a countable dense subset [tex]\{f_n\}[/tex] of X* and choose [tex]x_n\in X[/tex] such that for each n, we have [tex]||x_n||=1[/tex] and [tex]|f_n(x)|\geq(1/2)||f_n||[/tex].

Ok so what do I do now. We want to show that X is separable, so it's countable dense subset would be [tex]\{x_n\}[/tex], which we just have to show is dense in X, how do I do this?

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

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

# Problem on seperable banach spaces

Loading...

Similar Threads - Problem seperable banach | Date |
---|---|

I Problems in Differential geometry | Aug 18, 2017 |

I Problem when solving example with differential forms | Apr 9, 2017 |

I Levi-Civita: very small problem, need two steps explained | Sep 23, 2016 |

Problem with definition of tensor | May 18, 2015 |

Examples for seperation axioms. | Feb 12, 2008 |

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