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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

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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