The density property for JB*-triples

Seán Dineen; Michael Mackey; Pauline Mellon

Studia Mathematica (1999)

  • Volume: 137, Issue: 2, page 143-160
  • ISSN: 0039-3223

Abstract

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We obtain conditions on a JB*-algebra X so that the canonical embedding of X into its associated quasi-invertible manifold has dense range. We prove that if a JB* has this density property then the quasi-invertible manifold is homogeneous for biholomorphic mappings. Explicit formulae for the biholomorphic mappings are also given.

How to cite

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Dineen, Seán, Mackey, Michael, and Mellon, Pauline. "The density property for JB*-triples." Studia Mathematica 137.2 (1999): 143-160. <http://eudml.org/doc/216680>.

@article{Dineen1999,
abstract = {We obtain conditions on a JB*-algebra X so that the canonical embedding of X into its associated quasi-invertible manifold has dense range. We prove that if a JB* has this density property then the quasi-invertible manifold is homogeneous for biholomorphic mappings. Explicit formulae for the biholomorphic mappings are also given.},
author = {Dineen, Seán, Mackey, Michael, Mellon, Pauline},
journal = {Studia Mathematica},
keywords = {-algebra; -triples; quasi-invertible manifold; biholomorphic mappings},
language = {eng},
number = {2},
pages = {143-160},
title = {The density property for JB*-triples},
url = {http://eudml.org/doc/216680},
volume = {137},
year = {1999},
}

TY - JOUR
AU - Dineen, Seán
AU - Mackey, Michael
AU - Mellon, Pauline
TI - The density property for JB*-triples
JO - Studia Mathematica
PY - 1999
VL - 137
IS - 2
SP - 143
EP - 160
AB - We obtain conditions on a JB*-algebra X so that the canonical embedding of X into its associated quasi-invertible manifold has dense range. We prove that if a JB* has this density property then the quasi-invertible manifold is homogeneous for biholomorphic mappings. Explicit formulae for the biholomorphic mappings are also given.
LA - eng
KW - -algebra; -triples; quasi-invertible manifold; biholomorphic mappings
UR - http://eudml.org/doc/216680
ER -

References

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  1. [1] S. Dineen and P. Mellon, Holomorphic functions on symmetric Banach manifolds of compact type are constant, Math. Z., to appear. Zbl0937.46042
  2. [2] J. Dorfmeister, Algebraic systems in differential geometry, in: Jordan Algebras, de Gruyter, Berlin, 1994, 9-33. Zbl0816.53003
  3. [3] H. Hanche-Olsen and E. Størmer, Jordan Operator Algebras, Pitman, Boston, 1984. 
  4. [4] W. Holsztyński, Une généralisation du théorème de Brouwer sur les points invariants, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12 (1964), 603-606. Zbl0135.22902
  5. [5] W. Kaup, Algebraic characterization of symmetric complex Banach manifolds, Math. Ann. 228 (1977), 39-64. Zbl0335.58005
  6. [6] W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 138 (1983), 503-529. Zbl0519.32024
  7. [7] W. Kaup, Hermitian Jordan triple systems and automorphisms of bounded symmetric domains, in: Non-Associative Algebra and Its Applications, Kluwer, Dordrecht, 1994, 204-214. Zbl0810.46075
  8. [8] O. Loos, Bounded symmetric domains and Jordan pairs, lecture notes, Univ. of California at Irvine, 1977. 
  9. [9] O. Loos, Homogeneous algebraic varieties defined by Jordan pairs, Monatsh. Math. 86 (1978), 107-127. Zbl0404.14020
  10. [10] J.-I. Nagata, Modern Dimension Theory, North-Holland, Amsterdam, 1985. 
  11. [11] M. A. Rieffel, Dimension and stable rank in the K-theory of C*-algebras, Proc. London Math Soc. 46 (1983), 301-333. 
  12. [12] C. E. Rickart, Banach Algebras, Van Nostrand, Princeton, 1960. 
  13. [13] H. Upmeier, Symmetric Banach Manifolds and Jordan C*-Algebras, North-Holland, Amsterdam, 1985. 
  14. [14] K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov and A. I. Shirshov, Rings That Are Nearly Associative, Academic Press, 1982. 

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