Abstract

We calculate the characteristic of monotonicity of Orlicz-Lorentz function spaces ΛΦ,ω\Lambda_{\Phi,\omega}. Since degenerate Orlicz functions φ and degenerate weight functions ω are also admitted, this investigations concern the most possible wide class of Orlicz-Lorentz function spaces. These results concern both cases - an infinite and a finite non-atomic measure space, although in case of the finite measure the results are much more interesting. Let us recall that calculating of the characteristic of monotonicity of a Banach lattice is of great interest because of the result of A. Betiuk-Pilarska and S. Prus ["Banach lattices which are order uniformly noncreasy", J. Math. Anal. Appl. 342 (2008) 1271-1279] stating that if a Banach lattice X has this characteristic strictly smaller then 1 and X is weakly orthogonal, then it has the weak fixed point property (see W. A. Kirk and B. Sims, "Handbook of metric fixed point theory", Kluwer Academic Publishers (2001)).

Author information

Contact details are reproduced from the original publication and may be historical.

Paweł Foralewski

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

katon@amu.edu.pl

Henryk Hudzik

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

hudzik@amu.edu.pl

Radosław Kaczmarek

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

radekk@amu.edu.pl

Miroslav Krbec

Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, Czech Republic

Marek Wójtowicz

Institute of Mathematics, Casimir the Great University, Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland

mwojt@ukw.edu.pl

Keywords

  • Banach lattice
  • Köthe space
  • Orlicz-Lorentz space
  • Luxemburg norm
  • modulus of monotonicity
  • characteristic of monotonicity
  • strict monotonicity
  • uniform monotonicity
  • weak fixed point property
  • weak orthogonality

Mathematics Subject Classification

46B42, 46B20, 46A80, 46E30

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Suggested citation

P. Foralewski, H. Hudzik, R. Kaczmarek, M. Krbec, M. Wójtowicz. “On the Moduli and Characteristic of Monotonicity in Orlicz-Lorentz Function Spaces.” Journal of Convex Analysis 20 (2013), No. 4, 955–970. https://doi.org/10.68381/jca20052

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