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Non-commutative spectral theory for affine function spaces on convex sets

About this Title

Erik M. Alfsen and Frederic W. Shultz

Publication: Memoirs of the American Mathematical Society
Publication Year: 1976; Volume 6, Number 172
ISBNs: 978-0-8218-1872-5 (print); 978-1-4704-0756-8 (online)
DOI: https://doi.org/10.1090/memo/0172
MathSciNet review: 0412822

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Table of Contents

Chapters

  • 1. Smooth projections
  • 2. Projective units and projective faces
  • 3. Geometric properties of projective faces
  • 4. The lattice of $P$-projections
  • 5. Compatibility
  • 6. Existence of spectral resolutions
  • 7. Uniqueness of spectral resolutions
  • 8. Functional calculus
  • 9. Abelian subspaces
  • 10. Spectral convex sets
  • 11. Applications to operator algebras
  • 12. Some further results on spaces in spectral duality and on Jordan structure