On the local spectral subspace preservers Youssef Bouramdane

Abstract

Let $\mathcal{B}(X)$ be the algebra of all bounded linear operators on a complex Banach space $X$ with $\dim X \geq 3$. In this paper, we characterize the maps from $\mathcal{B}(X)$ into itself which preserves the dimension of the local spectral subspace relative to $\{1\}$ of the product of operators. The form of the maps from $\mathcal{B}(X)$ into itself preserving the local spectral subspace relative to $\{1\}$ of the product of operators are also described.