Let X be a complex Banach space and let \(x_{0}\in X\) be a fixed nonzero vector. Denote by \(\mathcal {L}\left( X\right) \) the algebra of all linear and bounded operators on X, and for \(T \in \mathcal {L}\left( X\right) \) denote by \(\sigma _{T}\left( x_{0}\right) \) the local spectrum of T at \(x_{0}\). We characterize linear and surjective maps \(\varphi :\mathcal {L} \left( X\right) \rightarrow \mathcal {L}\left( X\right) \) such that \(\varphi \left( I\right) \in \mathcal {L}\left( X\right) \) is invertible and

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令X为复Banach空间，令\（x_ {0} \ in X \）为固定的非零向量。表示由\（\ mathcal {L} \左（X \右）\）的所有线性的代数和上界运营商X，以及用于\（T \在\ mathcal {L} \左（X \右）\）用\（\ sigma _ {T} \ left（x_ {0} \ right）\）表示T在\（x_ {0} \）的局部频谱。我们刻画线性映射和射影映射\（\ varphi：\ mathcal {L} \ left（X \ right）\ rightarrow \ mathcal {L} \ left（X \ right）\）使得\（\ varphi \ left（I \ right）\ in \ mathcal {L} \ left（X \ right）\）是可逆的，

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