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The Banach-Lie Group of Lie Automorphisms of an H * -Algebra

Antonio J. Calderón MartínCandido Martín González — 2007

Bollettino dell'Unione Matematica Italiana

We study the Banach-Lie group 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 Aut ( A - ) 0 = Aut ( A ) implying Der ( A ) = Der ( A - ) . In the finite dimensional case Aut ( A - ) 0 is a direct product of Aut ( A ) and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.

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