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Finite von Neumann Algebras and Masas

Part of London Mathematical Society Lecture Note Series

  • Date Published: July 2008
  • availability: In stock
  • format: Paperback
  • isbn: 9780521719193

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  • A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann algebras. The theory of singular masas and Sorin Popa’s methods of constructing singular and semi-regular masas in general separable II1 factor are explored. Appendices cover the ultrapower of an II1 factor and the properties of unbounded operators required for perturbation results. Proofs are given in considerable detail and standard basic examples are provided, making the book understandable to postgraduates with basic knowledge of von Neumann algebra theory.

    • First book devoted to the general theory of finite von Neumann algebras
    • Contains large amount of current research, yet accessible to any postgraduate student in the area of operator algebras
    • Detailed discussion of masas, a topic not previously discussed in book form
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    Reviews & endorsements

    "Sinclair and Smith's monograph is very well written..."
    Paul Jolissaint, Mathematical Reviews

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    Product details

    • Date Published: July 2008
    • format: Paperback
    • isbn: 9780521719193
    • length: 410 pages
    • dimensions: 227 x 151 x 21 mm
    • weight: 0.56kg
    • availability: In stock
  • Table of Contents

    General introduction
    1. Masas in B(H)
    2. Finite von Neumann algebras
    3. The basic construction
    4. Projections and partial isometries
    5. Normalisers, orthogonality, and distances
    6. The Pukánszky invariant
    7. Operators in L
    8. Perturbations
    9. General perturbations
    10. Singular masas
    11. Existence of special masas
    12. Irreducible hyperfinite subfactors
    13. Maximal injective subalgebras
    14. Masas in non-separable factors
    15. Singly generated II1 factors
    Appendix A. The ultrapower and property Γ
    Appendix B. Unbounded operators
    Appendix C. The trace revisited
    Index.

  • Authors

    Allan Sinclair, University of Edinburgh
    Allan M. Sinclair is a Professor Emeritus in the School of Mathematics at the University of Edinburgh.

    Roger Smith, Texas A & M University
    Roger R. Smith is a Professor in the Department of Mathematics at Texas A&M University.

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