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PreprintarXiv licencearXiv

Amalgam approach to compactness in (quasi-)Banach function spaces

  • Dalimil Peša
  • Ivan Kotalík
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Abstract

We present amalgam-type characterisations of compactness in quasi-Banach function spaces. We further treat, in the same spirit, several related topics, namely convergence, (uniform) absolute continuity of the norm, and almost-compact embeddings. We also treat the case of rearrangement-invariant spaces and show that most of our conditions can be formulated in terms of the non-increasing rearrangement and the representation space.

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Cite

BibTeXRIS
BibTeX
@misc{pesa2026amalgam,
  title = {{Amalgam approach to compactness in (quasi-)Banach function spaces}},
  author = {Dalimil Peša and Ivan Kotalík},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.25419},
  eprint = {2606.25419},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.25419},
}
RIS
TY  - UNPB
TI  - Amalgam approach to compactness in (quasi-)Banach function spaces
AU  - Dalimil Peša
AU  - Ivan Kotalík
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2606.25419
UR  - https://arxiv.org/abs/2606.25419
AB  - We present amalgam-type characterisations of compactness in quasi-Banach function spaces. We further treat, in the same spirit, several related topics, namely convergence, (uniform) absolute continuity of the norm, and almost-compact embeddings. We also treat the case of rearrangement-invariant spaces and show that most of our conditions can be formulated in terms of the non-increasing rearrangement and the representation space.
ER  -