Compactness in Lorentz sequence spaces
DOI:
https://doi.org/10.12775/TMNA.2025.044Keywords
Lorentz sequence spaces, compactness criteria, equinormed setsAbstract
In this paper we are going to discuss compactness in Lorentz sequence spaces. Firstly, it will be shown how to define such a space, check whether a sequence belongs to it and calculate its norm. Equipped with this knowledge, we will proceed to propose usable compactness criteria for Lorentz sequence spaces, employing the concept of seminorms.References
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S. Chander, G. Datt and S. Verma, Operators on Lorentz sequence spaces, Math. Bohem. 134 (2009), no. 1, 87–98.
L. Grafakos, Classical Fourier Analysis, Springer, 2014.
J. Gulgowski, P. Kasprzak and P. Maćkowiak, Compactness in normed spaces: a unified approach through semi-norms, Topol. Methods Nonlinear Anal. 62 (2023), 105–134.
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I:Sequence Spaces, Springer, Berlin, Heidenberg, 2013.
G.G. Lorentz, Some new functional spaces, Ann. Math. 51 (1950), no. 1, 37–55.
Published
2026-05-18
How to Cite
1.
SAWICKI, Paweł. Compactness in Lorentz sequence spaces. Topological Methods in Nonlinear Analysis. Online. 18 May 2026. pp. 1 - 16. [Accessed 4 June 2026]. DOI 10.12775/TMNA.2025.044.
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