Abstract
Let \(\mathcal {H}\) be a complex Hilbert space of dimension \(\ge 2\) and \(\mathfrak {B}(\mathcal {H})\) be the algebra of all bounded linear operators on \(\mathcal {H}\). We give the form of surjective maps on \(\mathfrak {B}(\mathcal {H})\) preserving the c-numerical range of operator products when the maps preserve weak zero products. As a result, we obtain the characterization of surjective maps on \(M_n(\mathbb {C})\) preserving the c-numerical range of operator products. The proof of the results depends on some propositions of operators in \(\mathfrak {B}(\mathcal {H})\), which are of different interest.
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Acknowledgements
The authors wish to give their thanks to the referees for their worthy comments. This work is partially supported by National Natural Science Foundation of China (11371279, 11871375), Fundamental Research Funds for the Central Universities.
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Communicated by Fuad Kittaneh.
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Zhang, Y., Fang, X. The c-numerical range of operator products on \({\mathcal {B}}(H)\). Banach J. Math. Anal. 14, 163–180 (2020). https://doi.org/10.1007/s43037-019-00022-4
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DOI: https://doi.org/10.1007/s43037-019-00022-4