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.

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Commutative Dilation Theory

  • C. Ambrozie,
  • V. Müller

摘要

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.