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A note on the imbedding theorem of Browder and Ton


Author: J. Berkovits
Journal: Proc. Amer. Math. Soc. 131 (2003), 2963-2966
MSC (2000): Primary 47H05, 78M99
Published electronically: April 9, 2003
MathSciNet review: 1974355
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Abstract: The imbedding theorem of Browder and Ton states that for any real separable Banach space $X$ there exist a real separable Hilbert space $H$ and a compact linear injection $\psi:H\to X$ such that $\psi(H)$ is dense in $X.$ We shall give a short and elementary new proof to this result. We also briefly discuss the corresponding result without the completeness assumption.


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Additional Information

J. Berkovits
Affiliation: Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland
Email: juha.berkovits@oulu.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07094-1
Keywords: Compact imbedding
Received by editor(s): May 30, 2002
Published electronically: April 9, 2003
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society