**Memoirs of the American Mathematical Society**

2001;
114 pp;
Softcover

MSC: Primary 46; 81;

Print ISBN: 978-0-8218-2632-4

Product Code: MEMO/149/709

List Price: $56.00

Individual Member Price: $33.60

**Electronic ISBN: 978-1-4704-0300-3
Product Code: MEMO/149/709.E**

List Price: $56.00

Individual Member Price: $33.60

# Cocycles of CCR Flows

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*B. V. Rajarama Bhat*

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.

#### Table of Contents

# Table of Contents

## Cocycles of CCR Flows

- Contents vii8 free
- 1 Introduction 112 free
- 2 Compressions and dilations 617 free
- 3 Minimal dilation and induced semigroup 1526
- 4 Domination for E[sub(0)]-semigroups 2738
- 5 Compression under domination 3344
- 6 Units 4354
- 7 Cocycle computation for CCR flows 5465
- 8 Factorization theorem 6980
- 9 Hudson-Parthasarathy cocycles 8293
- Appendix A: Continuity 95106
- Appendix B: Discrete case 102113
- References 107118

#### Readership

Graduate students and research mathematicians interested in functional analysis.