arXiv subjects

Junxiang Qi

Publications and source records attributed to Junxiang Qi.

6 recordsLinked to original sources

arXiv2026

A Fermat--Torricelli convex-hull characterization of inner-product spaces via Birkhoff--James orthogonality

The classical location problem posed by Weber [Über den Standort der Industrien,Tübingen: J. C. B. Mohr, 1909] has motivated various geometric characterizations of inner-product spaces. Benítez, Fernández and Soriano [Trans. Amer. Math. Soc. \textbf{354} (2002), 5027--5038] characterized real inner-product spaces through the convex-hull property of Fermat--Torricelli medians.Pakhrou [J. Funct. Anal. \textbf{285} (2023), 110078] further established a characterization using $γ$-centers and equilateral triangles. Building on these results, we show that the Fermat--Torricelli convex-hull criterion remains valid when restricted to triples satisfying a one-sided Birkhoff--James orthogonality condition.The proof combines norming functionals, radial rescaling,Alexandrov differentiability, and the area formula.No completeness, smoothness, or strict convexity assumptions are required.

math.FA↗

arXiv2026

The Operator Daugavet Property in Semifinite Noncommutative $L_1$-Spaces

Let $\mathcal M$ be a diffuse semifinite von Neumann algebra endowed with a faithful normal semifinite trace $τ$. We prove that, for every nonzero Banach space $Y$, the projective tensor product $L_1(\mathcal M,τ)\widehat{\otimes}_πY$ has the operator Daugavet property. Moreover, the witnessing operators may always be chosen contractive. This extends the operator Daugavet phenomenon from atomless vector-valued $L_1$-spaces to the semifinite noncommutative setting and yields further Daugavet-type consequences for projective symmetric tensor products, all without approximation assumptions.

math.OA↗

arXiv2026

Nonembedding of Lorentz sequence spaces into Lorentz function spaces

Let $0<p, q<\infty$ with $p \neq q$, and suppose that $p<2$ or $q \leq 1$. We prove that the Lorentz sequence space $\ell_ {p, q}$ does not isomorphically embed into $L_ {p, q}(0,1)$. Consequently, $L_ {p, q}(0, \infty)$ does not isomorphically embed into $L_ {p, q}(0,1)$.

math.FA↗

arXiv2026

Birkhoff-Orthogonal Takahashi-von Neumann-Jordan Type Constants in Banach Spaces

In this paper, we introduce a new family of geometric constants CtB(X) of Birkhoff-orthogonal Takahashi-von Neumann-Jordan type for real Banach spaces. We discuss their basic properties and give a characterization of uniformly non-square spaces via CtB(X). Some sufficient conditions for super-reflexivity and fixed point property are presented. We establish upper bounds of CtB(X) related to orthogonal geometric moduli and constants, and obtain the sharp value for Radon planes.

math.FA↗

arXiv2026

A weighted Birkhoff orthogonal James-type constant

Let $X$ be a real Banach space and $λ\in[0,1]$. Motivated by orthogonal versions of the James constant, we introduce the weighted Birkhoff orthogonal James-type constant $$J_λ^{\perp}(X)=\sup \left\{\min \{\|λx+(1-λ) y\|,\|λx-(1-λ) y\|\}: x, y \in S_X, x \perp_B y\right\},$$ where $λ\in[0,1]$ and $x \perp_B y$ stands for Birkhoff orthogonality. We establish its basic bounds, stability properties, and reduction principles, and clarify its relations with the orthogonal James constant $J_{\perp}(X)$. The 2 -Lipschitz continuity of $J_λ^{\perp}(X)$ with respect to $λ$ is proved. New characterizations of uniformly nonsquare spaces are obtained; in particular, $J_λ^{\perp}(X)=1$ for some $λ\in(0,1)$ if and only if $X$ is not uniformly nonsquare. We also discuss connections with strict convexity, uniform convexity, modulus of smoothness, and the von Neumann-Jordan constant.

math.FA↗

arXiv2026

Generalized geometric constants related to Birkhoff orthogonality in Banach spaces

In this paper, based on Birkhoff orthogonality, we introduce two geometric constants $\boldsymbol{A}_{\boldsymbol{t}}^{\boldsymbol{B}}(\boldsymbol{X})$ and $\boldsymbol{D}_{\boldsymbol{t}}^{\boldsymbol{B}}(\boldsymbol{X})$ in Banach spaces, which generalize the skew geometric constants related to Birkhoff orthogonality. We systematically investigate the basic properties of the two constants, including their upper and lower bounds, and establish the equivalent characterizations for Banach spaces being uniformly non-square. Additionally, we explore the relationship between $\boldsymbol{D}_{\boldsymbol{t}}^{\boldsymbol{B}}(\boldsymbol{X})$ and the modulus of convexity $\boldsymbolδ_{\boldsymbol{X}}(\boldsymbol{\varepsilon})$. Finally, we explore several applications of the two newly proposed geometric constants.

math.FA↗