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Commutative Dilation Theory

In: Operator Theory

Author

Listed:
  • Caline Ambrozie

    (Institute of Mathematics, Academy of Czech Republic)

  • Vladimír Müller

    (Mathematical Institute, Academy of Sciences of the Czech Republic)

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

Suggested Citation

  • Caline Ambrozie & Vladimír Müller, 2015. "Commutative Dilation Theory," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 40, pages 1093-1124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_58
    DOI: 10.1007/978-3-0348-0667-1_58
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