Abstract
The theorem that each derivation of aC*-algebra\(\mathfrak{A}\) extends to an inner derivation of the weak-operator closure ϕ(\(\mathfrak{A}\))− of\(\mathfrak{A}\) in each faithful representation ϕ of\(\mathfrak{A}\) is proved in sketch and used to study the automorphism group of\(\mathfrak{A}\) in its norm topology. It is proved that the connected component of the identity ı in this group contains the open ball ℬ of radius 2 with centerl and that each automorphism in ℬ extends to an inner automorphism of ϕ(\(\mathfrak{A}\))−.
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Research conducted with the partial support of the NSF and ONR.
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Kadison, R.V., Ringrose, J.R. Derivations and automorphisms of operator algebras. Commun.Math. Phys. 4, 32–63 (1967). https://doi.org/10.1007/BF01645176
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DOI: https://doi.org/10.1007/BF01645176