Linear preservers of parallel matrix pairs with respect to the k-numerical radius

2024/08/28 by Bojan Kuzma, Chi-Kwong Li, Kuzma, Bojan +5 · 2 citations
Computer Science · Engineering · Mathematics · #15A60 #15A86 #47A12 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2408.16066

openalex publication_date 2024/08/28 · openalex created_date 2024/09/22 · openalex updated_date 2026/07/28

Abstract

Let 1 ≤ k < n be integers. Two n × n matrices A and B form a parallel pair with respect to the k-numerical radius w_k if w_k(A + μB) = w_k(A) + w_k(B) for some scalar μ with |μ| = 1; they form a TEA (triangle equality attaining) pair if the preceding equation holds for μ= 1. We classify linear bijections on \mathbb M_n and on \mathbb H_n which preserve parallel pairs or TEA pairs. Such preservers are scalar multiples of w_k-isometries, except for some exceptional maps on \mathbb H_n when n=2k.

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• Linear maps on L(ℓ_pⁿ,ℓ_p^m), (p∈ \1,∞\) preserving parallel pairs
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