Memoirs of the American Mathematical Society 2001; 114 pp; softcover Volume: 149 ISBN10: 0821826328 ISBN13: 9780821826324 List Price: US$53 Individual Members: US$31.80 Institutional Members: US$42.40 Order Code: MEMO/149/709
 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. Readership 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
 HudsonParthasarathy cocycles
 Appendix A. Continuity
 Appendix B. Discrete case
 References
