AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
Decompositions of operator algebras. I
About this Title
I. E. Segal
Publication: Memoirs of the American Mathematical Society
Publication Year:
1951; Number 9
ISBNs: 978-0-8218-1209-9 (print); 978-1-4704-0039-2 (online)
DOI: https://doi.org/10.1090/memo/0009
MathSciNet review: 0044749
Table of Contents
Chapters
- Volume I
- 1. Introduction
- 2. Definitions and notations
- 3. Decomposition of a state relative to a commutative algebra
- 4. Direct integrals of Hilbert spaces
- 5. Maximal decompositions
- Part I. Applications
- 6. Decomposition of a $W^*$-algebra into factors
- 7. Decomposition of a group representation into irreducible representations
- 8. Decomposition of an invariant measure into ergodic parts
- 9. The Fourier transform for separable unimodular groups
- 10. Deflation of decompositions
- Volume II. Multiplicity theory
- 1. Introduction
- Part I. Commutative algebras
- 2. Definitions and technical preliminaries
- 3. Structure of maximal abelian $W^*$-algebras
- 4. Structure of commutative $W^*$-algebras
- 5. Unitary invariants of commutative $W^*$-algebras and of $SA$ operators
- 6. Applications
- Part II. Non-commutative algebras
- 7. Decomposition theory
- 8. Algebras of uniform multiplicity
- 9. Algebras of type I