International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 28063, 3 pages
doi:10.1155/IJMMS/2006/28063
A new proof of a lemma by Phelps
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.
Abstract
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 f−1(0) and g−1(0) sufficiently close together, then either ‖f−g‖ or ‖f+g‖ must be small. We also extend this result to a complex
Banach space.