Compactness in Lorentz sequence spaces
DOI:
https://doi.org/10.12775/TMNA.2025.044Słowa kluczowe
Lorentz sequence spaces, compactness criteria, equinormed setsAbstrakt
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.Bibliografia
M. Ciesielski and G. Lewicki, Sequence Lorentz spaces and their geometric structure, J. Geom. Anal. 29 (2019), 1929–1952.
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.
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Prawa autorskie (c) 2026 Paweł Sawicki
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
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