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.
Andô, Tsuyoshi. "On a pair of commutative contractions." Acta Sci. Math. (Szeged) 24 (1963): 88-90.
Arhancet, Cédric, and Stephan Fackler, and Christian Le Merdy. "Isometric dilations and H1 calculus for bounded analytic semigroups and Ritt operators." Trans. Amer. Math. Soc. 369, no. 10 (2017): 6899-6933.
Ball, Joseph A., and Haripada Sau. "Rational dilation of tetrablock contractions revisited." J. Funct. Anal. 278, no. 1 (2020): 108275, 14 pp.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.