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, MHAMED and SABER, SOMAYA
(2021)
"Preservers of the local spectral radius zero of Jordan product of operators,"
Turkish Journal of Mathematics: Vol. 45:
No.
2, Article 29.
https://doi.org/10.3906/mat-2010-88
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss2/29
