If ${\mathscr H}$ is a Hilbert space, $\varphi$ is a (not necessary linear)
$*$-surjective mapping on ${\mathbb B}({\mathscr H})$ and $\varphi$ preserves the spectrum
of operators of the form $ABA^{*}$, then $\varphi$ is either an algebra automorphism or an
algebra anti-automorphism.
Publié le : 2010-05-15
Classification:
Spectrum,
rank one operator,
trace functional,,
operator algebra,
automorphism,
anti-automorphism,
47B49,
46L05,
47L30
@article{1302268212,
author = {Jelodar, Ali Taghavi and Moslehian, Mohammad Sal and Sanami, Abolfazl},
title = {A ternary characterization of automorphisms of ${\mathbb B}({\mathscr H})$},
journal = {Nihonkai Math. J.},
volume = {21},
number = {1},
year = {2010},
pages = { 1-9},
language = {en},
url = {http://dml.mathdoc.fr/item/1302268212}
}
Jelodar, Ali Taghavi; Moslehian, Mohammad Sal; Sanami, Abolfazl. A ternary characterization of automorphisms of ${\mathbb B}({\mathscr H})$. Nihonkai Math. J., Tome 21 (2010) no. 1, pp. 1-9. http://gdmltest.u-ga.fr/item/1302268212/