Abstract
Let \({{\mathcal B}(H)}\) be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space \({H}\). In this paper, we get a complete classification of surjective linear maps on \({{\mathcal B}(H)}\) that preserve quadratic operators in both directions. An analogue result in the setting of finite-dimensional Banach spaces is given.
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Oudghiri, M., Souilah, K. Linear Preservers of Quadratic Operators. Mediterr. J. Math. 13, 4929–4938 (2016). https://doi.org/10.1007/s00009-016-0783-8
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DOI: https://doi.org/10.1007/s00009-016-0783-8