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arXiv · 0911.5559

Minimal sequences and the Kadison-Singer problem

W. Lawton
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Abstract

The Kadison-Singer problem asks: does every pure state on the diagonal sublgebra of the C*-algebra of bounded operators on a separable infinite dimensional Hilbert space admit a unique extension? A yes answer is equivalent to several open conjectures including Feichtinger's: every bounded frame is a finite union of Riesz sequences. We consider the special case: Feichtinger's conjecture for exponentials and prove that the set of projections onto a measurable subset of the circle group of the set of exponential functions equals a union of a finite number of Reisz sequences if and only if there exists a Reisz subsequence corresponding to integers whose characteristic function is a nonzero minimal sequence.

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W. Lawton. 2009-11-30. Minimal sequences and the Kadison-Singer problem. https://arxiv.org/abs/0911.5559

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