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
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.
- Anna Denkowska
- Cracow University of Economics, Department of Mathematics, Rakowiecka 27, 31-510 Cracow, Poland
- Received: 2013-02-11.
- Accepted: 2013-03-09.
