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arXiv · 2609.37503

Von Neumann-Jordan Constants in Banach Tensor Products

Wenwen Zhang·Ying Xu·Qi Liu·Yongjin Li
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Abstract

We investigate the von Neumann--Jordan constant of Banach tensor products equipped with the injective and projective tensor norms. We first establish lower estimates in terms of the geometric properties of the factor spaces and show that, whenever both factors are infinite-dimensional, the von Neumann--Jordan constants of both canonical tensor products attain the maximal value \(2\). For finite-dimensional factors, we obtain explicit results for classical sequence spaces and characterize the extremal case through operator-space and orthogonal-contact conditions. We further derive dimension-sensitive estimates based on Euclidean sections. Finally, we study the constant under equivalent renormings and determine its exact renorming envelope for injective and projective tensor products. As consequences, we characterize when these tensor products are superreflexive and when they are weak Hilbert spaces. These results clarify the influence of tensor norms, dimension, and renorming on the von Neumann--Jordan geometry of Banach tensor products.

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Wenwen Zhang, Ying Xu, Qi Liu, Yongjin Li. 2026-09-27. Von Neumann-Jordan Constants in Banach Tensor Products. https://arxiv.org/abs/2609.37503

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