A new proof of a lemma by Phelps

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.