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Lithuanian Mathematical Journal

, Volume 55, Issue 2, pp 263–269 | Cite as

Probability structures in subspace lattice approach to foundations of quantum theory

  • Ekaterina Turilova
Article
  • 43 Downloads

Abstract

Noncommutative measure and probability theory develops parallel to classical probability theory. In our paper, we summarize recent results on the structure of subspaces affiliated with von Neumann algebras and noncommutative measures defined on them. We show the interplay of ideas from classical and noncommutative measure theories based on general inner product spaces and bring new examples in this area.

Keywords

affiliated subspaces von Neumann algebras noncommutative measures 

MSC

46L10 46L51 46S10 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Information TechnologyKazan Federal UniversityKazanRussia

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