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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Buhagiar, D. Chetcuti, E. and Dvurečenskij, A. 2011. Quasi-splitting subspaces and Foulis-Randall subspaces. Journal of Mathematical Physics, Vol. 52, Issue. 12, p. 123508.


    Buhagiar, David Chetcuti, Emmanuel and Dvurečenskij, Anatolij 2009. On Gleason’s Theorem without Gleason. Foundations of Physics, Vol. 39, Issue. 6, p. 550.


    Buhagiar, David Chetcuti, Emmanuel and Dvurečenskij, Anatolij 2007. Handbook of Quantum Logic and Quantum Structures.


    Chetcuti, E. and Dvurečenskij, A. 2005. Recent Progress on Pre-Hilbert-Space Logics and Their Measure Spaces. International Journal of Theoretical Physics, Vol. 44, Issue. 12, p. 2177.


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THE STATE-SPACE OF THE LATTICE OF ORTHOGONALLY CLOSED SUBSPACES

  • E. CHETCUTI (a1) and A. DVUREČENSKIJ (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089504002174
  • Published online: 01 January 2005
Abstract

The notion of a strongly dense inner product space is introduced and it is shown that, for such an incomplete space $S$ (in particular, for each incomplete hyperplane of a Hilbert space), the system $F(S)$ of all orthogonally closed subspaces of $S$ is not stateless, and the state-space of $F(S)$ is affinely homeomorphic to the face consisting of the free states on the projection lattice corresponding to the completion of $S$. The homeomorphism is determined by the extension of the states. In particular, when $S$ is complex, the state-space of $F(S)$ is affinely homeomorphic to the state-space of the Calkin algebra associated with $\skew3\overline S$.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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