Abstract
The central result of this paper is a method of characterizing those commuting tuples of operators that have a unitary dilation, in terms of the existence of a positive map with certain properties. Although this positivity condition is not necessarily easy to check given a concrete example, it can be used to find practical tests in some circumstances. As an application, we extend a dilation theorem of Sz.-Nagy and Foiaş concerning regular dilations to a more general setting
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Robert Archer, J. (2006). Positivity and the Existence of Unitary Dilations of Commuting Contractions. In: Dritschel, M.A. (eds) The Extended Field of Operator Theory. Operator Theory: Advances and Applications, vol 171. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7980-3_2
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DOI: https://doi.org/10.1007/978-3-7643-7980-3_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7979-7
Online ISBN: 978-3-7643-7980-3
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