On the structure of commuting isometries
Karel Horák, Vladimír Müller (1987)
Commentationes Mathematicae Universitatis Carolinae
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Karel Horák, Vladimír Müller (1987)
Commentationes Mathematicae Universitatis Carolinae
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Vladimír Kordula (1993)
Czechoslovak Mathematical Journal
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G. Van Dijk, M. Poel (1986)
Compositio Mathematica
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Eberhard Gerlach (1972)
Studia Mathematica
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Zbigniew Burdak, Wiesław Grygierzec (2020)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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The n-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an n-tuple. A series of such liftings leads to an isometric dilation of the n-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite n-tuple has an isometric dilation.