Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How do I show that a Banach space $X$ is reflexive if its dual $X'$ is reflexive without using any deep functional analysis theorems?

share|cite|improve this question
Could you be more precise when you say "deep functional analysis theorems"? Perhaps you could state (the names of) result that you are not willing to use. – matt Nov 7 '12 at 5:01
Also, you may find… helpful. – matt Nov 7 '12 at 5:02
I don't want to use Banach-Alaoglu-Bourbaki theorem, anything related to the Baire Category Theorem, or the Hanh-Banach Theorem. – Parakee Nov 7 '12 at 12:05
@Parkee then you should stop doing mathematics. I'm really hate question like "Prove everything without using anything." Well, one can do that, but this "proof" will repeat standard arguments of Hahn-Banach or Banach-Alaoglu or whatever else, and what is more it will be very long. – Norbert Nov 7 '12 at 17:00
@Parakee So what has developed your book? – Norbert Nov 7 '12 at 22:23

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.