Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Is every unit norm Bessel sequence in a Hilbert space a finite union of separated ones? Is every unit norm separated sequence a finite union of uniformly minimal (minimal with uniformly bounded biorthogonal vectors) ones?

share|improve this question
1  
It might be worth defining these terms... –  Matthew Daws Sep 15 '10 at 18:38
    
Unit norm means each vector is of norm 1. Separated means that there is a constant $c>0$ s.t. the distance between any two vectors is $>c$. Minimal means that none of the vectors is in the closed span of the others. –  MiM Sep 15 '10 at 19:23
    
And a Bessel sequence? –  Yemon Choi Sep 15 '10 at 21:57
    
$f_n$ is a Bessel sequence if $\sum|<f|f_n>|^2\leq \|f\|^2$ for all vectors $f$. –  MiM Sep 15 '10 at 22:21
    
instead of $\leq \|f\|^2$ it should be $\leq C\|f\|^2$. Sorry. –  MiM Sep 15 '10 at 22:23
add comment

1 Answer

Your questions are weakenings of the Feichtinger conjecture, which is equivalent to the Kadison-Singer problem. See

http://www.aimath.org/WWN/kadisonsinger/FrameProblems.pdf

and the references therein.

Your second question is Problem 2.2 there.

The questions themselves are not obvious ones. Why did you ask them?

share|improve this answer
add comment

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.