Abstract
It is shown that unitary extensions of a suitable isometry give a simple proof of the Nagy-Foias lifting theorem and lead directly to a Schur type analysis of contractive intertwining dilations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Adamjan, V. M; Arov, D.Z.; Krein, M. G.: Infinite Hankel matrices and Carathéodory-Féjer and Schur problems, Fund Anal and Appl 2 (1968), 1–17.
Arov, D. Z. and L. Z. Grossman: Scattering matrices in the theory of dilation of isometric operators, Soviet Math. DokJady 27 (1983), 518–522.
Arsene, Gr.; Ceausescu, Z.; Foias, C.: On intertwining dilations. VIII, J. Operator Theory 4 (1980), 55–91.
Arocena, R.: Generalized Toeplitz kernels and dilations of intertwining operators, Integral Fquations and Operator Theory 6 (1983), 759–778.
Arocena, R.: Schur analysis of a class of translation invariant forms, to appear in a volume in honor of M. Cotlar.
Arocena, R.: On a geometric interpretation of Schur parameters, preprint.
Arocena, R.: On the extension problem for a class of translation invariant forms, to appear in J Operator Theory.
Brodskii, V. M. and Ja. S. Shvartsman: On invariant subspaces of contractions, Soviet Math Doklady 12 (1971), 1659–1663.
Constantinescu, T.: A maximum entropy principle for contractive intertwining dilations, Operator Theory: Advances and Applications, 24(1987), 69–85.
Chumakin, M. E.: Generalized Resolvent of Isometric Operators, translated from Sibirskii Mat Zhurnah No. 4 ( 1967), 876–892.
Dym, H. and I. Gohberg: A maximum entropy principle for contractive interpolants, J. Fund. Anal. 65 (1986), 83–125.
Morán, M. D.: On intertwining operators, to appear in J. of Math Anal and Appl.
Nagy, B. Sz.-and C. Foias: Harmonic analysis of operators on Hilbert spaces, Amsterdam-Budapest, 1970.
Author information
Authors and Affiliations
Editor information
Additional information
To Professor Israel Gohberg, with admiration for his mathematical work as a researcher and as a teacher
Rights and permissions
Copyright information
© 1989 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Arocena, R. (1989). Unitary Extensions of Isometries and Contractive Intertwining Dilations. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 41. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9278-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9278-0_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9975-8
Online ISBN: 978-3-0348-9278-0
eBook Packages: Springer Book Archive