eBook ISBN: | 978-1-4704-0536-6 |
Product Code: | MEMO/199/930.E |
List Price: | $70.00 |
MAA Member Price: | $63.00 |
AMS Member Price: | $42.00 |
eBook ISBN: | 978-1-4704-0536-6 |
Product Code: | MEMO/199/930.E |
List Price: | $70.00 |
MAA Member Price: | $63.00 |
AMS Member Price: | $42.00 |
-
Book DetailsMemoirs of the American Mathematical SocietyVolume: 199; 2009; 101 ppMSC: Primary 60; Secondary 81
In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying \(E_0\)-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in \([0,1]\) or \(\mathbb R_+\). These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types \(\mathrm{I}_n\), \(\mathrm{II}_n\) and \(\mathrm{III}\) is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.
-
Table of Contents
-
Chapters
-
Chapter 1. Introduction
-
Chapter 2. Basics
-
Chapter 3. From product systems to random sets
-
Chapter 4. From random sets to product systems
-
Chapter 5. An hierarchy of random sets
-
Chapter 6. Direct integral representations
-
Chapter 7. Measurability in product systems: An algebraic approach
-
Chapter 8. Construction of product systems from general measure types
-
Chapter 9. Beyond separability: Random bisets
-
Chapter 10. An algebraic invariant of product systems
-
Chapter 11. Conclusions and outlook
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying \(E_0\)-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in \([0,1]\) or \(\mathbb R_+\). These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types \(\mathrm{I}_n\), \(\mathrm{II}_n\) and \(\mathrm{III}\) is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.
-
Chapters
-
Chapter 1. Introduction
-
Chapter 2. Basics
-
Chapter 3. From product systems to random sets
-
Chapter 4. From random sets to product systems
-
Chapter 5. An hierarchy of random sets
-
Chapter 6. Direct integral representations
-
Chapter 7. Measurability in product systems: An algebraic approach
-
Chapter 8. Construction of product systems from general measure types
-
Chapter 9. Beyond separability: Random bisets
-
Chapter 10. An algebraic invariant of product systems
-
Chapter 11. Conclusions and outlook