PreprintCC BY 4.0arXiv
Skew Schäffer Type Constants
Abstract
We introduce the skew Schäffer type constant as an infimal counterpart of the recently developed skew James type constant \cite{RaoWuLiuNiWang} and establish its basic geometric theory in Banach spaces. The new constant admits sharp universal bounds and characterizes uniform nonsquareness through a strict gap condition. Exact values are obtained in Hilbert and Lebesgue spaces, where an exact relation with the skew James type constant is established. We further derive a James-modulus estimate leading to sufficient conditions for uniform normal structure.
Related
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BibTeX
@misc{xu2026skew,
title = {{Skew Schäffer Type Constants}},
author = {Ying Xu and Qi Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03050},
eprint = {2610.03050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03050},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Skew Schäffer Type Constants
AU - Ying Xu
AU - Qi Liu
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03050
UR - https://arxiv.org/abs/2610.03050
AB - We introduce the skew Schäffer type constant as an infimal counterpart of the recently developed skew James type constant \cite{RaoWuLiuNiWang} and establish its basic geometric theory in Banach spaces. The new constant admits sharp universal bounds and characterizes uniform nonsquareness through a strict gap condition. Exact values are obtained in Hilbert and Lebesgue spaces, where an exact relation with the skew James type constant is established. We further derive a James-modulus estimate leading to sufficient conditions for uniform normal structure.
ER -