Dense $G_ \delta$’s contain orthonormal bases
HTML articles powered by AMS MathViewer
- by Richard Mercer PDF
- Proc. Amer. Math. Soc. 97 (1986), 449-452 Request permission
Abstract:
We show that a dense ${G_\delta }$ in the unit sphere of a Hilbert space necessarily contains an orthonormal basis. This allows us to choose an orthonormal basis of cyclic and separating vectors for a standard von Neumann algebra.References
- J. Dixmier and O. Maréchal, Vecteurs totalisateurs d’une algèbre de von Neumann, Comm. Math. Phys. 22 (1971), 44–50 (French, with English summary). MR 296708, DOI 10.1007/BF01651583
- S. Doplicher and R. Longo, Standard and split inclusions of von Neumann algebras, Invent. Math. 75 (1984), no. 3, 493–536. MR 735338, DOI 10.1007/BF01388641
- John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443, DOI 10.1007/978-1-4684-9339-9
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
- Stephen Willard, General topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0264581
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 449-452
- MSC: Primary 46C05; Secondary 46L10
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840627-9
- MathSciNet review: 840627