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Decompositions of operator algebras I and II / [electronic resource] I.E. Segal.

By: Material type: TextTextSeries: Memoirs of the American Mathematical Society ; no. 9.Publication details: Providence, R.I. : American Mathematical Society, 1989, c1951.Description: 1 online resource (66 p.)ISBN:
  • 9781470400392 (online)
Subject(s): Additional physical formats: Decompositions of operator algebras I and II /LOC classification:
  • QA3 .A57 no. 9
Online resources:
Contents:
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
Item type: E-BOOKS
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Includes bibliographical references.

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Mode of access : World Wide Web

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