Operator Theory

0447302 - MÚ 2016 RIV CH eng M - Monography Chapter
Ambrozie, Calin-Grigore - Müller, Vladimír
Commutative dilation theory.
Operator Theory. Basel: Springer, 2015 - (Alpay, D.), s. 1093-1124. ISBN 978-3-0348-0666-4
Institutional support: RVO:67985840
Keywords : commuting multioperator * dilation * von Neumann inequality
Subject RIV: BA - General Mathematics
http://link.springer.com/referenceworkentry/10.1007%2F978-3-0348-0667-1_58

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. Ando’s dilation and von Neumann inequality, 5. Spherical dilations, 6. Analytic models, 7. Further examples, 8. Concluding remarks.
Permanent Link: http://hdl.handle.net/11104/0249197