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Cocycles of CCR Flows
B. V. Rajarama Bhat, Indian Statistical Institute, Bangalore, India

Memoirs of the American Mathematical Society
2001; 114 pp; softcover
Volume: 149
ISBN-10: 0-8218-2632-8
ISBN-13: 978-0-8218-2632-4
List Price: US$56
Individual Members: US$33.60
Institutional Members: US$44.80
Order Code: MEMO/149/709
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We study the partially ordered set of quantum dynamical semigroups dominated by a given semigroup on the algebra of all bounded operators on a Hilbert space. For semigroups of \(*\)-endomorphisms this set can be described through cocycles. This helps us to prove a factorization theorem for dilations and to show that minimal dilations of quantum dynamical semigroups with bounded generators can be got through Hudson-Parthasarathy cocycles.


Graduate students and research mathematicians interested in functional analysis.

Table of Contents

  • Introduction
  • Compressions and dilations
  • Minimal dilation and induced semigroup
  • Domination for \(E_0\)-semigroups
  • Compression under domination
  • Units
  • Cocycle computation for CCR flows
  • Factorization theorem
  • Hudson-Parthasarathy cocycles
  • Appendix A. Continuity
  • Appendix B. Discrete case
  • References
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