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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Dense $ G\sb \delta$'s contain orthonormal bases


Author: Richard Mercer
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0840627-9
Keywords: Orthonormal basis, Baire category, dense $ {G_\delta }$, cyclic vector, separating vector
Article copyright: © Copyright 1986 American Mathematical Society