Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 104–113 | Cite as

Operator Analogy of Quantum Pseudo-Logic

  • M. Matvejchuk


In this paper, we study linear operators on real and complex Euclidean spaces which are real-orthogonal projections. It is a generalization of such standard (complex) orthogonal projections for which only the real part of scalar product vanishes. We note the difference between properties of real-orthogonal projections on real and on complex spaces. We can compare some partial order properties of orthogonal and of real-orthogonal projections. We prove that the set of all real-orthogonal projections in a finite-dimensional complex or real space is a quantum pseudo-logic.

Keywords and phrases

Hilbert space R-orthogonality projection partial order logic 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan National Research Technical UniversityKazanRussia

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