A Generalization of Ando's Theorem and Parrott's Example

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dc.creatorOpela, David
dc.date2005-05-09
dc.date.accessioned2026-07-07T05:19:43Z
dc.date.available2026-07-07T05:19:43Z
dc.descriptionAndo's theorem states that any pair of commuting contractions on a Hilbert space can be dilated to a pair of commuting unitaries. Parrott presented an example showing that an analogous result does not hold for a triple of pairwise commuting contractions. We generalize both of these results as follows. Any n-tuple of contractions that commute according to a graph without a cycle can be dilated to an n-tuple of unitaries that commute according to that graph. Conversely, if the graph contains a cycle, we construct a counterexample.
dc.description6 pages, accepted in PAMS
dc.identifierhttps://arxiv.org/abs/math/0505154
dc.identifierhttp://arxiv.org/abs/math/0505154
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75123
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject47A20
dc.titleA Generalization of Ando's Theorem and Parrott's Example
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