Geodesic
On fully *-extendable automorphisms of the unitary group of UHF-algebras
Ahmed Al Rawashdeh1 ; Ahmed Al Rawashdeh
1Department of Mathematical Sciences, UAEU United Arab Emirates University, Al-Ain, United Arab Emirates
Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 2, pp. 187-194 
Ahmed Al Rawashdeh; Ahmed Al Rawashdeh. On fully *-extendable automorphisms of the unitary group of UHF-algebras. Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 2, pp. 187-194. http://geodesic.mathdoc.fr/item/AMUC_2021_90_2_a4/
@article{AMUC_2021_90_2_a4,
     author = {Ahmed Al Rawashdeh and Ahmed Al Rawashdeh},
     title = { On fully *-extendable automorphisms of the unitary group of {UHF-algebras}},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {187--194},
     year = {2021},
     volume = {90},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2021_90_2_a4/}
}
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Voir la notice de l'article provenant de la source Comenius University

If $\varphi$ is an automorphism of the unitary group of UHF-algebras and the induced map $\theta_\varphi$ on the projections is an orthoisomorphism, then there exists a $*$-automorphism $\psi$ such that $\psi =\varphi$ on a subgroup containing $K_\infty$. Indeed, if $\varphi$ is a continuous, then $\varphi$ is implemented by a $*$-automorphism of the UHF-algebras. In this paper, we construct automorphisms of the unitary groups of certain UHF-algebras such that no $*$-automorphism coincides with $\varphi$ on the unitary group.