نوع مقاله : مقاله پژوهشی
عنوان مقاله English
نویسندگان English
Let $B(X)$ be the algebra of all bounded linear operators on infinite-dimensional complex Banachspace $X$.For
$T \in B(X)$ and $\lambda \in \mathbb{C}$, let $X_T(\{\lambda\})$ denotes the local spectral subspace of $T$ associated with $\{\lambda\}$. We show that if two additive maps $\varphi_1$ and $\varphi_2$ from $B(X)$ onto $B(X)$ satisfy X_{\varphi_1(T)\varphi_2(S)}(\{\lambda\}) = X_{T S}(\{\lambda\}) $
for all $T,S \in B(X)$ and $\lambda \in \mathbb{C}$, then there exists a bijective linear map $P : X \to X$
such that $\varphi_1(T) = T P^{-1}$ and $\varphi_2(T) = P T$ for all $T \in B(X)$.
Also, we obtain some interesting results in this direction.
کلیدواژهها English
