Schur product of matrices and numerical radius (range) preserving maps

Nonlinear maps preserving numerical radi

Nonlinear maps preserving numerical radius of indefinite skew products of operators

✍ Jinchuan Hou; Kan He; Xiuling Zhang 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 215 KB

Let H be a complex Hilbert space of dimension greater than 2 and J ∈ B(H) be an invertible self-adjoint operator. Denote by A † = J -1 A \* J the indefinite conjugate of A ∈ B(H) with respect to J and denote by w(A) the numerical radius of A. Let W and V be subsets of B(H) which contain all rank one