Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose $X$ is normed space. Prove that $X^\ast$ is rotund iff $X/M$ smooth whenever $M$ is a closed subspace of $X$ such that $X/M$ is two-dimensional. I know that "a normed space is smooth iff each of its two-dimensional subspaces is smooth.", maybe that will be used.

share|improve this question
    
In case it helps anybody with the context of this question, this seems to be Exercise 5.40, p.492 from Megginson's book Introduction to Banach Space Theory. @Strongart: I think it is useful to mention context (in this case the book or lecture notes which you are studying), since it might help people answering your question to see what are you supposed to know already for the exercise. –  Martin Sleziak Dec 26 '11 at 11:01

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.