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Continuous geometries with a transition probability

About this Title

John von Neumann

Publication: Memoirs of the American Mathematical Society
Publication Year: 1981; Volume 34, Number 252
ISBNs: 978-0-8218-2252-4 (print); 978-1-4704-0659-2 (online)
DOI: https://doi.org/10.1090/memo/0252
MathSciNet review: 634656
MSC: Primary 46L10; Secondary 06C20, 47D99, 52A50, 81B10

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Table of Contents

Chapters

  • I. The axioms
  • II. Geometrical character of $L$ and the ring $\mathcal {R}$
  • III. Unitary transformations
  • IV. Definiteness
  • V. Real traces
  • VI. Real traces and transition probabilities
  • VII. Completeness properties. Uniqueness of the real trace. The center
  • VIII. The operatorial description in a unitary space
  • IX. Construction of all systems $L$