## Abstract and Applied Analysis

### Contractive projections in Orlicz sequence spaces

Beata Randrianantoanina

#### 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 $AC^1$ and $AC^2$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 2 (2004), 133-145.

Dates
First available in Project Euclid: 6 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1081267504

Digital Object Identifier
doi:10.1155/S108533750431105X

Mathematical Reviews number (MathSciNet)
MR2058269

Zentralblatt MATH identifier
1079.46013

Subjects
Primary: 46B45: Banach sequence spaces [See also 46A45] 46B04

#### Citation

Randrianantoanina, Beata. Contractive projections in Orlicz sequence spaces. Abstr. Appl. Anal. 2004 (2004), no. 2, 133--145. doi:10.1155/S108533750431105X. https://projecteuclid.org/euclid.aaa/1081267504