Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (4): 1219-1226.doi: 10.1016/S0252-9602(10)60118-X

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THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN |H*-ALGEBRA

 A. J.Calderon Martí1, C.Martín González2   

  • Received:2007-11-10 Revised:2008-10-07 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Supported by the PCI of the UCA `Teorí a de Lie y Teor\'\i a de Espacios de Banach',  the PAI with project numbers FQM-298 and FQM-336, and  the project of the Spanish Ministerio de Educaci\'on y Ciencia MTM2004-06580-C02-02 and with fondos FEDER

Abstract:

We  study the Banach-Lie group Ltaut}(A) of Lie triple automorphisms of a complex associative H*-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder(A), are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut(A)0=Aut(A) implying Ltder(A)= Der(A). In the finite-dimensional case Ltaut(A)0 is a direct product of aut(A) and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.

Key words: Banach-Lie group, Lie triple automorphism, Lie triple derivation

CLC Number: 

  • 47B47
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