Contractive projections in Orlicz sequence spaces

Abstract

We characterize norm-one complemented subspaces of Orlicz sequence spaces ℓM equipped with either Luxemburg or Orlicz norm, provided that the Orlicz function M is sufficiently smooth and sufficiently different from the square function. We measure smoothness of M using AC1 and AC2 classes introduced by Maleev and Troyanski in 1991, and the condition for M to be different from a square function is essentially a requirement that the second derivative M″ of M cannot have a finite nonzero limit at zero. This paper treats the real case; the complex case follows from previously known results.