User mim - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T23:33:03Z http://mathoverflow.net/feeds/user/9257 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/38850/bessel-sequence-uniformly-minimal-separated Bessel sequence, uniformly minimal, separated MiM 2010-09-15T17:55:48Z 2010-09-16T11:34:55Z <p>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? </p> http://mathoverflow.net/questions/38850/bessel-sequence-uniformly-minimal-separated Comment by MiM MiM 2010-09-15T22:23:34Z 2010-09-15T22:23:34Z instead of $\leq \|f\|^2$ it should be $\leq C\|f\|^2$. Sorry. http://mathoverflow.net/questions/38850/bessel-sequence-uniformly-minimal-separated Comment by MiM MiM 2010-09-15T22:21:15Z 2010-09-15T22:21:15Z $f_n$ is a Bessel sequence if $\sum|&lt;f|f_n&gt;|^2\leq \|f\|^2$ for all vectors $f$. http://mathoverflow.net/questions/38850/bessel-sequence-uniformly-minimal-separated Comment by MiM MiM 2010-09-15T19:23:09Z 2010-09-15T19:23:09Z Unit norm means each vector is of norm 1. Separated means that there is a constant $c&gt;0$ s.t. the distance between any two vectors is $&gt;c$. Minimal means that none of the vectors is in the closed span of the others.