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
Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica
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.
@article{BUMI_2007_8_10B_3_a10,
author = {Calder\'on Mart{\'\i}n, Antonio J. and Mart{\'\i}n Gonz\'alez, Candido},
title = {The {Banach-Lie} {Group} of {Lie} {Automorphisms} of an $H^*${-Algebra}},
journal = {Bollettino della Unione matematica italiana},
pages = {623--631},
publisher = {mathdoc},
volume = {Ser. 8, 10B},
number = {3},
year = {2007},
zbl = {1145.46033},
mrnumber = {2351534},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a10/}
}
TY - JOUR AU - Calderón Martín, Antonio J. AU - Martín González, Candido TI - The Banach-Lie Group of Lie Automorphisms of an $H^*$-Algebra JO - Bollettino della Unione matematica italiana PY - 2007 SP - 623 EP - 631 VL - 10B IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a10/ LA - en ID - BUMI_2007_8_10B_3_a10 ER -
%0 Journal Article %A Calderón Martín, Antonio J. %A Martín González, Candido %T The Banach-Lie Group of Lie Automorphisms of an $H^*$-Algebra %J Bollettino della Unione matematica italiana %D 2007 %P 623-631 %V 10B %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a10/ %G en %F BUMI_2007_8_10B_3_a10
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/