Abstract
In this chapter a general theory for contractive operators is developed. Such operators may be viewed as compressions of isometric and unitary operators. The minimal isometric and minimal unitary dilations of a given contraction are to a large extent unique, which implies that those operators are useful instruments for the analysis of contractions. In this chapter we also prove the commutant lifting theorem and present some of its applications to interpolation problems.
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© 1993 Springer Basel AG
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Gohberg, I., Kaashoek, M.A., Goldberg, S. (1993). Dilation Theory. In: Classes of Linear Operators Vol. II. Operator Theory Advances and Applications, vol 63. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8558-4_9
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DOI: https://doi.org/10.1007/978-3-0348-8558-4_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9679-5
Online ISBN: 978-3-0348-8558-4
eBook Packages: Springer Book Archive