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Gleason-Type Theorem for Linear Spaces over the Field of Four Elements

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Abstract

We prove an analog of the famous Gleason theoremfor additive functions on the orthomodular poset of allprojections defined on an n-dimensional linear spaceover the field consisting of four elements. An essential part of the proof consists in acomputer calculation.

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REFERENCES

  • Gleason, A. M. (1957). Measures on the closed subspaces of a Hilbert space, Journal of Mathematics and Mechanics, 6, 885–894.

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  • Mushtari, D. (1989). Projection logics in Banach spaces, Izvestiya Vysshikh Uchebnykh Zavedenii. Seriya Matematika, No. 8, 59–70.

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  • Mushtari, D. (1995). Gleason-type theorems for signed measures on orthomodular posets of projections on linear spaces, International Journal of Theoretical Physics, 34, 1627–1635.

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Authors
  1. Daniar Mushtari
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Mushtari, D. Gleason-Type Theorem for Linear Spaces over the Field of Four Elements. International Journal of Theoretical Physics 37, 127–130 (1998). https://doi.org/10.1023/A:1026625625353

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  • DOI: https://doi.org/10.1023/A:1026625625353

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