Journal of Operator Theory

Volume 35, Issue 1, Winter 1996 pp. 117-132.

On commutant lifting with finite defect

Authors: Rodrigo Arocena (1), Tomas Ya. Azizov (2), Aad Dijksma (3) and Stefania A.M. Marcantognini (4)
Author institution:(1) Facultad de Ciencias, Universidad de la Republica, José M. Montero 3006, ap. 503, Montevideo, URUGUAY, e-mail: rarocena@cmat.edu.uy
(2) Department of Mathematics, Voronezh State University, Universitetskaja pl., 1, 394693 Voronezh, RUSSIA, e-mail: azizov@mathd.vucnit.voronezh.su
(3) Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, THE NETHERLANDS, e-mail: a.dijksma@math.rug.nl
(4) Department of Mathematics, Simón Bolívar University, Apart. Postal 89000, Caracas 1086-A, VENEZUELA, e-mail: stefania@usb.ve

Summary: In this note we generalize a theorem of J.A. Ball and W.J. Helton on commutant lifting with finite defect to a Kreĭn space setting. The proof of the generalization is based on an invariant subspace theorem.

Keywords: Kreĭn space, contraction, dilation, fixed point.

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