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Cocycles of CCR Flows

B. V. Rajarama Bhat Indian Statistical Institute, Bangalore, India
Available Formats:
Electronic ISBN: 978-1-4704-0300-3
Product Code: MEMO/149/709.E
List Price: $56.00 MAA Member Price:$50.40
AMS Member Price: $33.60 Click above image for expanded view Cocycles of CCR Flows B. V. Rajarama Bhat Indian Statistical Institute, Bangalore, India Available Formats:  Electronic ISBN: 978-1-4704-0300-3 Product Code: MEMO/149/709.E  List Price:$56.00 MAA Member Price: $50.40 AMS Member Price:$33.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1492001; 114 pp
MSC: 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 Hudson-Parthasarathy 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. Hudson-Parthasarathy cocycles
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Volume: 1492001; 114 pp
MSC: 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 Hudson-Parthasarathy 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. Hudson-Parthasarathy cocycles
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