Holomorphic automorphisms and collective compactness in J*-algebras of operator

José Isidro

Open Mathematics (2007)

  • Volume: 5, Issue: 3, page 512-522
  • ISSN: 2391-5455

Abstract

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Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball B 𝔄 in a J*-algebra 𝔄 of operators. Let 𝔉 be the family of all collectively compact subsets W contained in B 𝔄 . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family 𝔉 is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when 𝔄 is a Cartan factor.

How to cite

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José Isidro. "Holomorphic automorphisms and collective compactness in J*-algebras of operator." Open Mathematics 5.3 (2007): 512-522. <http://eudml.org/doc/269061>.

@article{JoséIsidro2007,
abstract = {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.},
author = {José Isidro},
journal = {Open Mathematics},
keywords = {J*-algebras; Cartan factors; holomorphic automorphisms; Banach-Lie groups; collective compactness},
language = {eng},
number = {3},
pages = {512-522},
title = {Holomorphic automorphisms and collective compactness in J*-algebras of operator},
url = {http://eudml.org/doc/269061},
volume = {5},
year = {2007},
}

TY - JOUR
AU - José Isidro
TI - Holomorphic automorphisms and collective compactness in J*-algebras of operator
JO - Open Mathematics
PY - 2007
VL - 5
IS - 3
SP - 512
EP - 522
AB - 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.
LA - eng
KW - J*-algebras; Cartan factors; holomorphic automorphisms; Banach-Lie groups; collective compactness
UR - http://eudml.org/doc/269061
ER -

References

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