Let X be an infinite-dimensional Banach space and let $B\left(X\right)$ denote the algebra of all bounded linear operators on X. For $T\in B\left(X\right)$ the sets ${\sigma }_1\left(T\right)=\{\lambda \in \sigma (T)\mid T-\lambda I\text{ is a semi-Fredholm operator}\},$ ${\sigma }_2\left(T\right)=\{\lambda \in \sigma (T)\mid T-\lambda I\text{ is a Fredholm operator}\},$ and ${\sigma }_3\left(T\right)=\{\lambda \in \sigma (T)\mid T-\lambda I\text{ is a Weyl operator}\}$ are called, respectively, the semi-Fredholm domain, the Fredholm domain, and the Weyl domain of T in the spectrum, $\sigma \left(T\right)$. We characterize surjective maps on $B\left(X\right)$ (with no additivity assumption) leaving invariant ${\sigma }_i\left(TS\right)$ or ${\sigma }_i\left(TST\right)$ for all $T,S\in B\left(X\right)$ and $i\in \{1,2,3\}$.

令X为无限维Banach空间，令$乙（X）$表示X上所有有界线性算子的代数。对于$Ť\in 乙（X）$ 集合 ${\sigma }_{\mathrm{1个}}（Ť）=\{\lambda \in \sigma （Ť）\mid Ť-\lambda \mathrm{一世}\text{ 是半弗雷德霍尔姆运算符}\}，$ ${\sigma }_2（Ť）=\{\lambda \in \sigma （Ť）\mid Ť-\lambda \mathrm{一世}\text{ 是Fredholm的运营商}\}，$ 和 ${\sigma }_3（Ť）=\{\lambda \in \sigma （Ť）\mid Ť-\lambda \mathrm{一世}\text{ 是Weyl运算符}\}$被称为分别半Fredholm型结构域，所述结构域的Fredholm，以及外尔域Ť在光谱，$\sigma （Ť）$。我们在上刻画射影图$乙（X）$ （无可加性假设）不变量 ${\sigma }_{\mathrm{一世}}（Ť\mathrm{小号}）$ 要么 ${\sigma }_{\mathrm{一世}}（Ť\mathrm{小号}Ť）$ 对所有人 $Ť，\mathrm{小号}\in 乙（X）$ 和 $\mathrm{一世}\in \{\mathrm{1个}，2，3\}$。