arXiv subjects

M. Elhodaibi

Publications and source records attributed to M. Elhodaibi.

2 recordsLinked to original sources

arXiv2024

Comment on Maps preserving the dimension of fixed points of products of operators

Let $\mathcal{B} (X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$. In this note, we show that a lemma used in the proof of the main result of [ Taghavi and Hosseinzadeh, linear and Multilinear algebra (2013) 1285-1292.] has an incorrect proof. Then, instead of such a lemma, we provide two elementary lemmas to obtain a proof of Taghavi and Hosseinzadeh's main result free of errors.

math.FA↗

arXiv2022

Jordan product and analytic core preservers

Let $\mathcal{B} (X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$. For an operator $ T \in \mathcal{B} (X)$, $K(T)$ denotes as usual the analytic core of $T$. We determine the form of surjective maps $ \phi $ on $ \mathcal{B} (X)$ satisfying $$ K(\phi(T) \phi(S) + \phi (S) \phi (T)) = K(TS + ST) $$ for all $T, S \in \mathcal{B} (X)$.

math.FA↗