@article {
author = {Niazi Motlagh, Abolfazl},
title = {On the Norm of Jordan $*$-Derivations},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {1},
pages = {104-107},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2019.97176},
abstract = {Let $\mathcal H$ be a complex Hilbert space and let $B(\mathcal H)$ be the algebra of all bounded linear operators on $\mathcal H$. Let $T\in\ B(\mathcal H)$.In this paper, we determine the norm of the inner Jordan $*$-derivation $\Delta_T:X\mapsto TX-X^*T$ acting on the Banach algebra $B(\mathcal{H})$. More precisely, we show that $$\big{\|}\Delta_T\big{\|}\geq 2\sup_{\lambda\in W_0(T)}|{\rm Im}(\lambda)|$$in which $W_0(T)$ is the maximal numerical range of operator $T$.},
keywords = {Jordan$*$-derivation,Numerical Range,maximal numerical range},
url = {http://www.kjm-math.org/article_97176.html},
eprint = {http://www.kjm-math.org/article_97176_b3a4d842feb70c384bb0001e22fc2e2b.pdf}
}