Nonlinear maps preserving higher-dimensional numerical ranges of Jordan $$*$$-products

Abstract

Let H and K be complex Hilbert spaces. Denote by B(H ) and B(K ) the algebras of all bounded linear operators on H and K , respectively. In this paper, we characterize that nonlinear map φ : B(H ) → B(K ) that preserves the higher-dimensional numerical ranges of Jordan * -products. KeywordsHigher-dimensional numerical range • Nonlinear map • Jordan η- * -product Mathematics Subject Classification 47B49 • 46L10 B Chaoqun Chen