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PreprintCC BY-NC-ND 4.0arXiv

The Uniform Primary Factorisation Property for C(K,E)

  • Antonio Acuaviva
  • Pablo Acuaviva
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Abstract

Let K be an uncountable compact metrizable space, and E be a separable Banach space with the uniform primary factorisation property (UPFP) and containing no isomorphic copy of c0. We prove that $C(K, E)$ also has the UPFP. As a consequence, we obtain the primariness of the bi-parameter spaces C([0,1],ℓp) and C([0,1], Lp) for 1 ≤ p<∞.

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Cite

BibTeXRIS
BibTeX
@misc{acuaviva2026uniform,
  title = {{The Uniform Primary Factorisation Property for $C(K,E)$}},
  author = {Antonio Acuaviva and Pablo Acuaviva},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18993},
  eprint = {2609.18993},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18993},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The Uniform Primary Factorisation Property for C(K,E)
AU  - Antonio Acuaviva
AU  - Pablo Acuaviva
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.18993
UR  - https://arxiv.org/abs/2609.18993
AB  - Let K be an uncountable compact metrizable space, and E be a separable Banach space with the uniform primary factorisation property (UPFP) and containing no isomorphic copy of c_0. We prove that $C(K, E)$ also has the UPFP. As a consequence, we obtain the primariness of the bi-parameter spaces C([0,1],ℓ_p) and C([0,1], L_p) for 1 ≤ p<∞.
ER  -