Dvurečenskij, Anatolij Frame functions, signed measures and completeness of inner product spaces. (English) Zbl 0715.46031 Acta Univ. Carol., Math. Phys. 30, No. 2, 41-49 (1989). Summary: We show that an inner product space is complete iff it possesses at least one nonzero frame function, or, equivalently, when and only when some systems of closed subspaces possess at least one nonzero signed measure. Cited in 5 Documents MSC: 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) Keywords:an inner product space is complete iff it possesses at least one nonzero frame function; systems of closed subspaces possess at least one nonzero signed measure PDFBibTeX XMLCite \textit{A. Dvurečenskij}, Acta Univ. Carol., Math. Phys. 30, No. 2, 41--49 (1989; Zbl 0715.46031) Full Text: EuDML