Opuscula Math. 33, no. 4 (2013), 667-684

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.

Full text (pdf)

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

Cite this article as:
Anna Denkowska, Contractive and optimal sets in Musielak-Orlicz spaces with a smoothness condition, Opuscula Math. 33, no. 4 (2013), 667-684, http://dx.doi.org/10.7494/OpMath.2013.33.4.667

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.