Abstract
In this chapter we study isometric and unitary dilations. These concepts are due to Sz.-Nagy and they have no analogue in linear algebra, that is, they are genuinely infinite dimensional concepts. Indeed their natural framework is that of infinite dimensional Hilbert spaces. From now on we assume that the reader is acquainted with elementary facts concerning operators in Hilbert space, as presented in [RieszSz.-N].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes and Comments
Frazho, A.E., A shift operator approach to state affine system theory, IEEE Trans. Automat. Control, 17 (1982) pp. 117–122.
Frazho, A.E., Models for noncommuting operators, J. Functional Analysis, 48 (1982) pp. 1–11.
Frazho, A.E. and D.K. Lee A pole placement procedure via H°° optimization, The 26 Annual Allerton Conference, Sept. (1988) pp. 872–880.
Fuhrmann, P.A., A functional calculus in Hilbert space based on operator valued analytic functions, Israel J. Math., 6 (1968) pp. 267–278.
Golub, G.H. and C.F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 1983.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Basel AG
About this chapter
Cite this chapter
Foias, C., Frazho, A.E. (1990). Isometric and Unitary Dilations. In: The Commutant Lifting Approach to Interpolation Problems. OT 44 Operator Theory: Advances and Applications, vol 44. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7712-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7712-1_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7714-5
Online ISBN: 978-3-0348-7712-1
eBook Packages: Springer Book Archive