Bessel sequence, uniformly minimal, separated - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T19:30:06Z http://mathoverflow.net/feeds/question/38850 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/38921#38921 Answer by Bill Johnson for Bessel sequence, uniformly minimal, separated Bill Johnson 2010-09-16T03:32:04Z 2010-09-16T11:34:55Z <p>Your questions are weakenings of the Feichtinger conjecture, which is equivalent to the Kadison-Singer problem. See</p> <p><a href="http://www.aimath.org/WWN/kadisonsinger/FrameProblems.pdf" rel="nofollow">http://www.aimath.org/WWN/kadisonsinger/FrameProblems.pdf</a></p> <p>and the references therein.</p> <p>Your second question is Problem 2.2 there.</p> <p>The questions themselves are not obvious ones. Why did you ask them?</p>