Non-linear maps on self-adjoint operators preserving numerical radius and numerical range of Lie product

2014/11/21 by Kan He, He, Kan, Jinchuan Hou +1
Computer Science · Mathematics · #47A12 #47B49 #47H20 #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Operator Algebras (math.OA) #math.OA #msc:47A12 #msc:47B49 #msc:47H20

paper · pdf · doi:10.48550/arxiv.1411.5891

22 pages

arxiv created 2014/11/21 · openalex publication_date 2014/11/21 · arxiv updated 2014/11/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Let H be a complex separable Hilbert space of dimension ≥ 2, \mathcal B_s(H) the space of all self-adjoint operators on H. We give a complete classification of non-linear surjective maps on \mathcal B_s(H) preserving respectively numerical radius and numerical range of Lie product.

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