Abstract
We completely describe surjective maps preserving the peripheral local spectrum of Jordan product of operators. Let \(x_0 \in X\) and \(y_0 \in Y \) be two nonzero vectors. We show that a map \(\varphi \) from B(X) onto B(Y) satisfies
if and only if there exists a bijective bounded linear map from X into Y such that\( A(x_0)=y_0\) and either \(\varphi (T)=-ATA^{-1}\) for all \(T \in B(X) \) or \(\varphi (T)=ATA^{-1}\) for all \(T \in B(X)\).
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Sadeghi, H., Mirzapour, F. Peripheral Local Spectrum Preservers of Jordan Products of Operators. Bull. Iran. Math. Soc. 44, 437–456 (2018). https://doi.org/10.1007/s41980-018-0029-6
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DOI: https://doi.org/10.1007/s41980-018-0029-6