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

Kan He; Jinchuan Hou

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

Operator Algebras 2014-11-24 v1

Authors: Kan He , Jinchuan Hou

Abstract

Let $H$ be a complex separable Hilbert space of dimension $\geq 2$ , ${\mathcal B}_s(H)$ 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.

Keywords

self-adjoint operators non-linear maps numerical radius numerical range Lie product Hilbert space

Cite

@article{arxiv.1411.5891,
  title  = {Non-linear maps on self-adjoint operators preserving numerical radius and numerical range of Lie product},
  author = {Kan He and Jinchuan Hou},
  journal= {arXiv preprint arXiv:1411.5891},
  year   = {2014}
}

Comments

22 pages

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