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PMATH 810

Banach Algebras and Operator Theory

Graduate

Winter 2025 · Operator Algebras

Topics

  • Banach-space theorems
  • Banach algebras and functional calculus
  • Operators on Banach and Hilbert spaces
  • Compact operators
  • Gelfand transform and Jacobson radical
  • C*-algebras and GNS construction
  • von Neumann algebras and spectral theorem

Readings

  • C*-algebras and Operator Theory
    G. J. Murphy · recommended
    Academic Press, 1990
  • Banach Algebra Techniques in Operator Theory
    R. Douglas · recommended
    Academic Press, 1972
  • Fundamentals of the Theory of Operator Algebras
    R. Kadison and J. Ringrose · recommended
    Academic Press, 1983
  • Functional Analysis
    W. Rudin · recommended
    McGraw-Hill, 1977, as cited in outline
  • Theory of Operator Algebras
    M. Takesaki · recommended
    Springer, 1979
  • L. W. Marcoux course notes, made available on the instructor’s UW website: https://www.math.uwaterloo.ca/~lwmarcou/
    unspecified
Sources