On fully ∗-extendable automorphisms of the unitary group of uhf-algebras

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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.

Original languageEnglish
Pages (from-to)187-194
Number of pages8
JournalActa Mathematica Universitatis Comenianae
Issue number2
Publication statusPublished - 2021


  • And phrases
  • C-algebras; automorphisms

ASJC Scopus subject areas

  • General Mathematics


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