International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 28063, 3 pages

A new proof of a lemma by Phelps

Antonia E. Cardwell

Department of Mathematics, Millersville University of Pennsylvania, Millersville 17551-0302, PA, USA

Received 7 December 2005; Revised 3 May 2006; Accepted 7 May 2006

Copyright © 2006 Antonia E. Cardwell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give a different proof of a lemma by Phelps (1960) which asserts, roughly speaking, that if two norm-one functionals f and g have their hyperplanes f1(0) and g1(0) sufficiently close together, then either fg or f+g must be small. We also extend this result to a complex Banach space.