On the non-uniqueness of minimal projection in Lp spaces

The main objective of this note is to exhibit a simple example of subspaces U subset of L-p(mu) (p not equal 2) that admit two different projections with minimal norm. While for p = 1, infinity, such subspaces are well-known [W. Odyniec, G. Lewicki, Minimal Projections in Banach Spaces, in: Lecture Notes in Mathematics, vol. 1449, Springer-Verlag, Berlin, 1990. Problems of existence and uniqueness and their application], for 1 < p < infinity their existence was open. Published by Elsevier Inc.