Abstract
Let H be a complex Hilbert space with dim H ≥ 3, B s (H) the (real) Jordan algebra of all self-adjoint operators on H. Every surjective map Φ: B s (H) → B s (H) preserving numerical radius of operator products (respectively, Jordan triple products) is characterized. A characterization of surjective maps on B s (H) preserving a cross operator norm of operator products (resp. Jordan triple products of operators) is also given.
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Supported by National Science Foundation of China (Grant Nos. 10771157, 10871111), the Provincial Science Foundation of Shanxi (Grant No. 2007011016) and the Research Fund of Shanxi for Returned Scholars (Grant No. 2007-38)
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He, K., Hou, J.C. & Zhang, X.L. Maps preserving numerical radius or cross norms of products of self-adjoint operators. Acta. Math. Sin.-English Ser. 26, 1071–1086 (2010). https://doi.org/10.1007/s10114-010-9001-y
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DOI: https://doi.org/10.1007/s10114-010-9001-y