Turkish Journal of Mathematics
Abstract
Let $\mathscr{B}(X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$, and denote by $r_{T}(x)$ the local spectral radius of any operator $T \in \mathscr{B}(X)$ at any vector $x \in X$. In this paper, we characterize surjective maps $\phi$ on $ \mathscr{B}(X)$ satisfying $ r_{\phi(T)\phi(A) + \phi(A)\phi(T)}(x)=0$ if and only if $ r_{TA+AT}(x)=0 $
DOI
10.3906/mat-2010-88
Keywords
Nonlinear preservers, quasinilpotent part, local spectral radius, Jordan product
First Page
1030
Last Page
1039
Recommended Citation
ELHODAIBI, M, & SABER, S (2021). Preservers of the local spectral radius zero of Jordan product of operators. Turkish Journal of Mathematics 45 (2): 1030-1039. https://doi.org/10.3906/mat-2010-88
