Electronic ISBN:  9781470403003 
Product Code:  MEMO/149/709.E 
List Price:  $56.00 
MAA Member Price:  $50.40 
AMS Member Price:  $33.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 149; 2001; 114 ppMSC: Primary 46; 81;
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 HudsonParthasarathy cocycles.
ReadershipGraduate students and research mathematicians interested in functional analysis.

Table of Contents

Chapters

1. Introduction

2. Compressions and dilations

3. Minimal dilation and induced semigroup

4. Domination for $E_0$semigroups

5. Compression under domination

6. Units

7. Cocycle computation for CCR flows

8. Factorization theorem

9. HudsonParthasarathy cocycles


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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 HudsonParthasarathy cocycles.
Graduate students and research mathematicians interested in functional analysis.

Chapters

1. Introduction

2. Compressions and dilations

3. Minimal dilation and induced semigroup

4. Domination for $E_0$semigroups

5. Compression under domination

6. Units

7. Cocycle computation for CCR flows

8. Factorization theorem

9. HudsonParthasarathy cocycles