Skip to main content

Advertisement

We’d like to understand how you use our websites in order to improve them. Register your interest.

Moduli and Characteristics of Monotonicity in Some Banach Lattices

Abstract

First the characteristic of monotonicity of any Banach lattice is expressed in terms of the left limit of the modulus of monotonicity of at the point . It is also shown that for Köthe spaces the classical characteristic of monotonicity is the same as the characteristic of monotonicity corresponding to another modulus of monotonicity . The characteristic of monotonicity of Orlicz function spaces and Orlicz sequence spaces equipped with the Luxemburg norm are calculated. In the first case the characteristic is expressed in terms of the generating Orlicz function only, but in the sequence case the formula is not so direct. Three examples show why in the sequence case so direct formula is rather impossible. Some other auxiliary and complemented results are also presented. By the results of Betiuk-Pilarska and Prus (2008) which establish that Banach lattices with and weak orthogonality property have the weak fixed point property, our results are related to the fixed point theory (Kirk and Sims (2001)).

Publisher note

To access the full article, please see PDF

Author information

Affiliations

Authors

Corresponding author

Correspondence to Henryk Hudzik.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Foralewski, P., Hudzik, H., Kaczmarek, R. et al. Moduli and Characteristics of Monotonicity in Some Banach Lattices. Fixed Point Theory Appl 2010, 852346 (2010). https://doi.org/10.1155/2010/852346

Download citation

Keywords

  • Differential Geometry
  • Computational Biology
  • Banach Lattice
  • Full Article
  • Publisher Note