Geodesic
The Banach-Lie Group of Lie Automorphisms of an $H^*$-Algebra
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 623-631.

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We study the Banach-Lie group $\operatorname{Aut}(A^-)$ of Lie automorphisms of a complex associative $H^*$-algebra. Also some consequences about its Lie algebra, the algebra of Lie derivations of $A$, are obtained. For a topologically simple $A$, in the infinite-dimensional case we have $\operatorname{Aut}(A^-)_0 = \operatorname{Aut}(A)$ implying $\operatorname{Der}(A) = \operatorname{Der}(A^-)$. In the finite dimensional case $\operatorname{Aut}(A^{-})_{0}$ is a direct product of $\operatorname{Aut}(A)$ and a certain subgroup of Lie derivations $\delta$ from $A$ to its center, annihilating commutators.
Studiamo il gruppo di Banach-Lie $\operatorname{Aut}(A^-)$ degli automorfismi di Lie di una $H^*$-algebra associativa complessa. Vengono anche ottenute alcune conseguenze riguardanti la sua algebra di Lie, cioè l'algebra delle derivazioni di Lie di $A$. Per una $A$ topologicamente semplice, nel caso di dimensione infinita si ha $\operatorname{Aut}(A^-)_0 = \operatorname{Aut}(A)$, il che implica che $\operatorname{Der}(A) = \operatorname{Der}(A^-)$. Nel caso di dimensione finita, $\operatorname{Aut}(A^-)_{0}$ è il prodotto diretto di $\operatorname{Aut}(A)$ e di un certo sottogruppo di derivazioni di Lie $\delta$ da $A$ al suo centro, che annullano i commutatori. 
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Calderón Martín, Antonio J.; Martín González, Candido. The Banach-Lie Group of Lie Automorphisms of an $H^*$-Algebra. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 623-631. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a10/

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