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2007 | 5 | 3 | 512-522
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Holomorphic automorphisms and collective compactness in J*-algebras of operator

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Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball $$B_\mathfrak{A} $$ in a J*-algebra $$\mathfrak{A}$$ of operators. Let $$\mathfrak{F}$$ be the family of all collectively compact subsets W contained in $$B_\mathfrak{A} $$ . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family $$\mathfrak{F}$$ is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when $$\mathfrak{A}$$ is a Cartan factor.
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Bibliografia
  • [1] P.M. Anselone and T.W. Palmer: “Collectively compact sets of linear operators“, Pac. J. Math., Vol. 25, (1968), pp. 417–422.
  • [2] L.A. Harris: “Bounded symmetric homogeneous domains in infinite-dimensional spaces“, In: Proceedings on Infinite Dimensional Holomorphy, Lecture Notes in Mathematics, Vol. 364, Springer-Verlag, 1974, pp. 13–40.
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  • [7] J.M. Isidro and L.L. Stachó: “Weakly and weakly** continuous elements in JBW*-triples“, Acta Sci. Math. (Szeged), Vol. 57, (1993), pp. 555–567.
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  • [12] L.L. Stachó and J.M. Isidro: “Algebraically compact elements in JB*-triples“, Acta Sci. Math. (Szeged), Vol. 54, (1990), pp. 171–190.
  • [13] H. Upmeier: “Symmetric Banach Manifolds and Jordan C*-Algebras“, In: North Holland Mathematics Studies, Vol. 104, North Holland, Amsterdam, 1985.
  • [14] J.P. Viguée and J.M. Isidro: “Sur la topologie du groupe des automorphismes analytiques d’un domaine cerclé borné”, B. Sci. Math., Vol. 106, (1982), pp. 417–426.
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bwmeta1.element.doi-10_2478_s11533-007-0016-2
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