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

top
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

top

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

top
  1. [1] P.M. Anselone and T.W. Palmer: “Collectively compact sets of linear operators“, Pac. J. Math., Vol. 25, (1968), pp. 417–422. Zbl0157.45202
  2. [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. 
  3. [3] L.A. Harris: “A generalization of C*-algebras“, P. Lond. Math. Soc., Vol. 42, (1981), pp. 331–361. http://dx.doi.org/10.1112/plms/s3-42.2.331 
  4. [4] L.A. Harris and W. Kaup: “Linear algebraic groups in infinite dimensions“, Illinois J.. Math., Vol. 21, (1977), pp. 666–674. Zbl0385.22011
  5. [5] T. Ho, J. Martinez Moreno, A. Peralta and B. Russo: “Derivations on real and complex JB*-triples“, J. Lond. Math. Soc., Vol. 65, (2002), pp. 85–102. http://dx.doi.org/10.1112/S002461070100271X Zbl1015.46041
  6. [6] J.M. Isidro and W. Kaup: “Weak continuity of holomorphic automorphisms in JB*-triples“, Math. Z., Vol. 210, (1992), pp. 277–288. http://dx.doi.org/10.1007/BF02571798 Zbl0812.46066
  7. [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. Zbl0834.17046
  8. [8] W. Kaup: “Uber die Automorphismen Grassmancher Mannigfaltigkeiten unendlicher Dimension“, Math. Z., Vol. 144, (1975), pp. 75–96. http://dx.doi.org/10.1007/BF01190938 Zbl0322.32014
  9. [9] W. Kaup: “A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces“, Math. Z., Vol. 183, (1983), pp. 503–529. http://dx.doi.org/10.1007/BF01173928 Zbl0519.32024
  10. [10] W. Kaup: “Hermitian Jordan Triple Systems and Automorphisms of Bounded Symmetric Domains“, In: Santoz González (Ed.): Non-Associative Algebras and Applications, Kluwer Academic Publishers, 1994, pp. 204–214. 
  11. [11] T.W. Palmer: “Totally bounded sets of precompact linear operators“, P. Am. Math. Soc., Vol. 20, (1969), pp. 101–106. http://dx.doi.org/10.2307/2035969 Zbl0165.47603
  12. [12] L.L. Stachó and J.M. Isidro: “Algebraically compact elements in JB*-triples“, Acta Sci. Math. (Szeged), Vol. 54, (1990), pp. 171–190. Zbl0736.46053
  13. [13] H. Upmeier: “Symmetric Banach Manifolds and Jordan C*-Algebras“, In: North Holland Mathematics Studies, Vol. 104, North Holland, Amsterdam, 1985. 
  14. [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. Zbl0546.32012

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.