On complete-cocomplete subspaces of an inner product space

In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space S is complete if and only if there exists a σ-additive state on C(S), the orthomodular poset of complete-cocomplete subspaces of S. We then consider the problem of w...

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Veröffentlicht in:	Applications of mathematics (Prague) 2005-04, Vol.50 (2), p.103-114
Hauptverfasser:	Buhagiar, David, Chetcuti, Emanuel
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of mathematics Completeness Constrictions Construction Criteria Hilbert space Hyperplanes Mathematical problems Splitting Studies Subspaces
Online-Zugang:	Volltext
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