Volume 33 • Number 2 • 2010   • Minimal Sequences and the Kadison-Singer Problem Wayne Lawton Abstract. The Kadison-Singer problem asks: does every pure state on the C*-algebra admit a unique extension to the C*-algebra ? A yes answer is equivalent to several open conjectures including Feichtinger's: every bounded frame is a finite union of Riesz sequences. We prove that for measurable is a finite union of Riesz sequences in if and only if there exists a nonempty such that is a minimal sequence and is a Riesz sequence. We also suggest some directions for future research. 2000 Mathematics Subject Classification: Primary: 37B10, 42A55, 46L05. Full text: PDF