TY - JOUR
T1 - On fully ∗-extendable automorphisms of the unitary group of uhf-algebras
AU - Al-Rawashdeh, A.
N1 - Publisher Copyright:
© 2021, Comenius University in Bratislava. All rights reserved.
PY - 2021
Y1 - 2021
N2 - If ϕ is an automorphism of the unitary group of UHF-algebras and the induced map θϕ on the projections is an orthoisomorphism, then there exists a ∗-automorphism ψ such that ψ = ϕ on a subgroup containing the self-adjoint unitaries in the finite dimensional subalgebras. Indeed, if ϕ is continuous, then ϕ 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 ϕ on the unitary group.
AB - If ϕ is an automorphism of the unitary group of UHF-algebras and the induced map θϕ on the projections is an orthoisomorphism, then there exists a ∗-automorphism ψ such that ψ = ϕ on a subgroup containing the self-adjoint unitaries in the finite dimensional subalgebras. Indeed, if ϕ is continuous, then ϕ 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 ϕ on the unitary group.
KW - And phrases
KW - C-algebras; automorphisms
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M3 - Article
AN - SCOPUS:85107309326
SN - 0862-9544
VL - 90
SP - 187
EP - 194
JO - Acta Mathematica Universitatis Comenianae
JF - Acta Mathematica Universitatis Comenianae
IS - 2
ER -