International Journal of Theoretical Physics

, Volume 27, Issue 9, pp 1059–1067

State on splitting subspaces and completeness of inner product spaces


  • Anatolij Dvurečenskij
    • Mathematical InstituteSlovak Academy of Sciences
  • Sylvia Pulmannová
    • Mathematical InstituteSlovak Academy of Sciences

DOI: 10.1007/BF00674351

Cite this article as:
Dvurečenskij, A. & Pulmannová, S. Int J Theor Phys (1988) 27: 1059. doi:10.1007/BF00674351


We show that an inner product spaceV is complete iff the system of all splitting subspaces, i.e., of all subspacesM for whichM + M=V, possesses at least one completely additive state.

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© Plenum Publishing Corporation 1988