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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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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Copyright (c) 2026 Paweł Sawicki
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