Opuscula Math. 33, no. 4 (2013), 667-684
http://dx.doi.org/10.7494/OpMath.2013.33.4.667

Opuscula Mathematica

# Contractive and optimal sets in Musielak-Orlicz spaces with a smoothness condition

Anna Denkowska

Abstract. In this paper we use our recent generalization of a theorem of Jamison-Kamińska-Lewicki (characterizing one-complemented subspaces in Musielak-Orlicz sequence spaces defined by Musielak-Orlicz functions satisfying a general smoothness condition) in order to compare contractive and optimal sets in finite-dimensional Musielak-Orlicz $$\ell^{(n)}_\Phi$$ spaces in the spirit of Kamińska-Lewicki. We also give an example illustrating the importance of the smoothness assumptions in our theorem.

Keywords: Musielak-Orlicz sequence spaces, one-complemented subspaces, contractive and optimal sets.

Mathematics Subject Classification: 46E30, 46B20.

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• Anna Denkowska
• Cracow University of Economics, Department of Mathematics, Rakowiecka 27, 31-510 Cracow, Poland