PreprintCC BY-NC-SA 4.0arXiv
Reflexive and strictly convex Banach spaces without Property (H)
Abstract
We prove that Property (H) fails for a broad class of reflexive strictly convex Banach spaces. More generally, the real Banach space (⨁j=1∞ Lpj(Ωj,μj))ℓs does not have Property (H) whenever 1≤ s<∞, 1≤ pj<∞, supj pj=+∞, and each Lpj(Ωj,μj) is infinite-dimensional.
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BibTeX
@misc{feng2026reflexive,
title = {{Reflexive and strictly convex Banach spaces without Property (H)}},
author = {Chunliu Feng and Geng Tian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23996},
eprint = {2609.23996},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23996},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Reflexive and strictly convex Banach spaces without Property (H)
AU - Chunliu Feng
AU - Geng Tian
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.23996
UR - https://arxiv.org/abs/2609.23996
AB - We prove that Property (H) fails for a broad class of reflexive strictly convex Banach spaces. More generally, the real Banach space (⨁_j=1^∞ L^p_j(Ω_j,μ_j))_ℓ^s does not have Property (H) whenever 1≤ s<∞, 1≤ p_j<∞, sup_j p_j=+∞, and each L^p_j(Ω_j,μ_j) is infinite-dimensional.
ER -