PreprintCC BY 4.0arXiv
Computable presentations of separable Lebesgue spaces
Abstract
For every right-c.e.\ real p∈(1,2), Lp[0,1] has a computable presentation. The proof combines an effective stability modulus for almost isometric embeddings with a Fra\"ıssé-style construction in which the exponent varies. In the same range, if ℓp has a computable presentation, then p is computable. Combining these with the known results gives the computable presentability classification for all separable Lebesgue spaces. We also formulate an effective Fra\"ıssé theorem for Banach spaces and apply it to obtain a computable presentation of the Gurarij Banach space.
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BibTeX
@misc{xie2026computable,
title = {{Computable presentations of separable Lebesgue spaces}},
author = {Ruofei Xie and Xuanheng Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30565},
eprint = {2610.30565},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30565},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Computable presentations of separable Lebesgue spaces
AU - Ruofei Xie
AU - Xuanheng Zhao
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30565
UR - https://arxiv.org/abs/2610.30565
AB - For every right-c.e.\ real p∈(1,2), L^p[0,1] has a computable presentation. The proof combines an effective stability modulus for almost isometric embeddings with a Fra\"ıssé-style construction in which the exponent varies. In the same range, if ℓ^p has a computable presentation, then p is computable. Combining these with the known results gives the computable presentability classification for all separable Lebesgue spaces. We also formulate an effective Fra\"ıssé theorem for Banach spaces and apply it to obtain a computable presentation of the Gurarij Banach space.
ER -