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Let H be a complex Hilbert space, B(H) be the algebra of all bounded linear operators on H, H(H) be the subset of all selfadjoint operators in B(H) and V = B(H) or H(H). Denote by w(A) the numerical radius of A ∈ B(H). We characterize surjective maps Φ: ν → V that satisfy w(Φ(A) - Φ(B)) = w(A - B) for all A, B ∈ V without the linearity assumption.

Numerical radius distance-preserving maps on $\mathcal {B}(H)$