Commutative Dilation Theory

Cǎlin Ambrozie () and Vladimir Müller ()
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Cǎlin Ambrozie: Institute of Mathematics – Romanian Academy
Vladimir Müller: Mathematical Institute AV CR

Chapter 42 in Operator Theory, 2026, pp 1225-1257 from Springer

Abstract: Abstract 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. This chapter gives a survey of dilation theory for commuting tuples of Hilbert space operators.

Keywords: Commuting multioperator; Dilation; Model; von Neumann inequality; Primary 47A13; Secondary 47A20; 47A45; 47-00 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_58

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