Strong Projections in Hilbert Space and Quantum Logic
- Authors: Matvejchuk M.S.1, Vladova E.V.2
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Affiliations:
- Kazan National Research Technical University
- Moscow State Technical University of Civil Aviation
- Issue: Vol 40, No 10 (2019)
- Pages: 1521-1531
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205733
- DOI: https://doi.org/10.1134/S1995080219100196
- ID: 205733
Cite item
Abstract
In the paper we study linear operators on complex Hilbert spaces which are strong real-orthogonal projections. It is a generalization of such standard (complex) orthogonal projections for which only the real part of scalar product vanishes. We compare order properties of the orthogonal and of the strong real-orthogonal projections. We prove that the set of all strong real-orthogonal the projections in the complex space is the quantum pseudo logic. We also prove an analogy of Gleason’s theorem.
Keywords
About the authors
M. S. Matvejchuk
Kazan National Research Technical University
Author for correspondence.
Email: Marjan.Matvejchuk@yandex.ru
Russian Federation, Kazan, 420111
E. V. Vladova
Moscow State Technical University of Civil Aviation
Author for correspondence.
Email: evv_03@mail.ru
Russian Federation, Moscow, 125993