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Automorphisms of quasitriangular algebras. (English) Zbl 0549.47024

The outer automorphism group of a nest algebra is canonically isomorphic to the (spatial) automorphism group of the nest itself. The outer automorphism group of the associated quasitriangular algebra is canonically isomorphic to a group of ”approximate” automorphisms of the nest. A simple proof that every derivation of a quasitriangular algebra is inner is obtained as a corollary.

MSC:

47L30 Abstract operator algebras on Hilbert spaces
47B47 Commutators, derivations, elementary operators, etc.
46H20 Structure, classification of topological algebras
47A15 Invariant subspaces of linear operators
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References:

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