Convex Bodies Associated to Tensor Norms

• Published in: arXiv.org
• Main Authors: Fernández-Unzueta, Maite, Higueras-Montaño, Luisa F
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 15.07.2018
• Subjects: Ellipsoids; Isomorphism; Mathematical analysis; Norms; Tensors

We determine when a convex body in \(\mathbb{R}^d\) is the closed unit ball of a reasonable crossnorm on \(\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l},\) \(d=d_1\cdots d_l.\) We call these convex bodies "tensorial bodies". We prove that, among them, the only ellipsoids are the clo...