Commutative Dilation Theory

Caline Ambrozie () and Vladimír Müller ()
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Caline Ambrozie: Institute of Mathematics, Academy of Czech Republic
Vladimír Müller: Mathematical Institute, Academy of Sciences of the Czech Republic

Chapter 40 in Operator Theory, 2015, pp 1093-1124 from Springer

Abstract: Abstract Dilation theory Dilation theory of single Hilbert space contractions is an important and very useful part of operator theory. By the main result of the theory, every Hilbert space contraction has the uniquely determined minimal unitary dilation. In many situations this enables to study instead of a general contraction its unitary dilation, which has much nicer properties.The present paper gives a survey of dilation theory for commuting tuples of Hilbert space operators. The paper is organized as follows: 1. Introduction 2. Dilation theory of single contractions 3. Regular dilations 4. The Ando dilation and von Neumann inequality 5. Spherical dilations 6. Analytic models 7. Further examples 8. Concluding remarks

Keywords: Dilation Theory; Ando Dilation; Unitary Dilation; Regular Dilatation; Single Contractions (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_58

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DOI: 10.1007/978-3-0348-0667-1_58

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