Contractive projections in Orlicz sequence spaces

Abstract

We characterize norm-one complemented subspaces of Orlicz sequence spaces ${\ell }_M$ 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 $A{C}^1$ and $A{C}^2$ 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.