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Title: Minimal sequences and the Kadison-Singer problem
Authors: Lawton, W. 
Keywords: Feichtinger conjecture
Riesz product
Riesz sequence
Syndetic set
Thue-morse minimal sequence
Issue Date: 2010
Citation: Lawton, W. (2010). Minimal sequences and the Kadison-Singer problem. Bulletin of the Malaysian Mathematical Sciences Society 33 (2) : 169-176. ScholarBank@NUS Repository.
Abstract: The Kadison-Singer problem asks: does every pure state on the C*-algebra ℓ∞ (Z) admit a unique extension to the C*-algebra β (ℓ2 (Z))? 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 S ⊂ T, {χS e2πikt}k∈Z is a finite union of Riesz sequences in L2 (T) if and only if there exists a nonempty A ⊂ Z such that χA is a minimal sequence and {χS e2πikt} k∈A is a Riesz sequence. We also suggest some directions for future research.
Source Title: Bulletin of the Malaysian Mathematical Sciences Society
ISSN: 01266705
Appears in Collections:Staff Publications

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