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arXiv:0908.1942 [math.LO]AbstractReferencesReviewsResources

Orthonormal bases of Hilbert spaces

Ilijas Farah

Published 2009-08-13, updated 2009-08-15Version 2

I prove that a Hilbert space has the property that each of its dense (not necessarily closed) subspaces contains an orthoormal basis if and only if it is separable.

Comments: The main result of the note has been known. See Orthonormal bases and quasi-splitting subspaces in pre-Hilbert spaces D. Buhagiar, E. Chetcuti, H. Weber, J. Math. Anal. Appl., 345 (2008) 725-730. and the references thereof. Thanks to Nigel Kalton to pointing this out
Categories: math.LO, math.FA
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