On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds

José Isidro

Open Mathematics (2007)

  • Volume: 5, Issue: 4, page 696-709
  • ISSN: 2391-5455

Abstract

top
The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.

How to cite

top

José Isidro. "On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds." Open Mathematics 5.4 (2007): 696-709. <http://eudml.org/doc/269372>.

@article{JoséIsidro2007,
abstract = {The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.},
author = {José Isidro},
journal = {Open Mathematics},
keywords = {Classical symmetric complex Banach manifolds; JB*-triples; Cartan factors; Banach-Lie algebras; Complete holomorphic vector fields; classical symmetric complex Banach manifolds; JB-triples; complete holomorphic vector fields},
language = {eng},
number = {4},
pages = {696-709},
title = {On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds},
url = {http://eudml.org/doc/269372},
volume = {5},
year = {2007},
}

TY - JOUR
AU - José Isidro
TI - On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds
JO - Open Mathematics
PY - 2007
VL - 5
IS - 4
SP - 696
EP - 709
AB - The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.
LA - eng
KW - Classical symmetric complex Banach manifolds; JB*-triples; Cartan factors; Banach-Lie algebras; Complete holomorphic vector fields; classical symmetric complex Banach manifolds; JB-triples; complete holomorphic vector fields
UR - http://eudml.org/doc/269372
ER -

References

top
  1. [1] T.J. Barton and Y. Friedman: “Bounded derivations of JB*-triples”, Quart. J. Math. Oxford Ser. 2, Vol. 41, (1990), pp. 255–268. http://dx.doi.org/10.1093/qmath/41.3.255 Zbl0728.46046
  2. [2] D. Beltită and M. Sabac: Lie algebras of bounded operators, Operator Theory: Advances and Applications, Vol. 120, Birkhäuser Verlag, Basel, 2001. Zbl1084.47500
  3. [3] P. Civin and B. Yood: “Lie and Jordan structures in Banach algebras”, Pacific J. Math., Vol. 15, (1965), pp. 775–797. Zbl0135.35701
  4. [4] J.B. Conway: A course in operator theory, Graduate Studies in Mathematics, Vol. 21, American Mathematical Society, Providence RI, 2000. Zbl0936.47001
  5. [5] S. Dineen and R.M. Timoney: “The centroid of a JB*-triple system”, Math. Scand., Vol. 62, (1988), pp. 327–342. Zbl0655.46044
  6. [6] C.K. Fong, C.R. Miers and A.R. Sourour: “Lie and Jordan ideals of operators on Hilbert space”, Proc. Amer. Math. Soc., Vol. 84, (1982), pp. 516–520. http://dx.doi.org/10.2307/2044026 Zbl0509.47035
  7. [7] C.K. Fong and G.J. Murphy: “Ideals and Lie ideals of operators”, Acta Sci. Math., Vol. 51, (1987), pp. 441–456. Zbl0659.47040
  8. [8] L.A. Harris: “Bounded symmetric homogeneous domains in infinite dimensional spaces”, Proceedings on Infinite Dimensional Holomorphy, Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973, pp. 13–40, Lecture Notes in Math., Vol. 364, Springer, Berlin, 1974. http://dx.doi.org/10.1007/BFb0069002 
  9. [9] F.J. Hervés and J.M. Isidro: “Isometries and automorphisms of the spaces of spinors”, Rev. Mat. Univ. Complut. Madrid, Vol. 5, (1992), pp. 193–200. Zbl0816.46045
  10. [10] T. Ho, J. Martinez-Moreno, A.M. Peralta and B. Russo: “Derivations on real and complex JB*-triples”, J. London. Math. Soc.(2), Vol. 65, (2002), pp. 85–102. http://dx.doi.org/10.1112/S002461070100271X Zbl1015.46041
  11. [11] 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
  12. [12] W. Kaup: “On real Cartan factors”, Manuscripta Math., Vol. 92, (1997), pp. 191–222. http://dx.doi.org/10.1007/BF02678189 Zbl0881.17033
  13. [13] M. Koecher: “Imbedding of Jordan algebras into Lie algebras I”, Amer. J. Math., Vol. 89, (1967), pp. 787–816. http://dx.doi.org/10.2307/2373242 Zbl0209.06801
  14. [14] M. Koecher: “Imbedding of Jordan algebras into Lie algebras II”, Amer. J. Math., Vol. 90, (1968), pp. 476–510. http://dx.doi.org/10.2307/2373540 Zbl0311.17005
  15. [15] O. Loos: Bounded symmetric domains and Jordan pairs, University of California at Irvine, Lecture Notes, 1997. Zbl0914.17011
  16. [16] K. Meyberg: “Jordan-Triplesysteme und die Koecher-Konstruktion von Lie-Algebren”, Math. Z., Vol. 115, (1970), pp. 58–78. http://dx.doi.org/10.1007/BF01109749 Zbl0186.34501
  17. [17] K. Meyberg: “Zur Konstruktion von Lie-Algebren aus Jordan-Triplesystemen”, Manuscripta Math., Vol. 3, (1970), pp. 115–132. http://dx.doi.org/10.1007/BF01273306 Zbl0211.35701
  18. [18] C.R. Miers: “Closed Lie ideals in operator algebras”, Canad. J. Math., Vol. 33, (1981), pp. 1271–1278. Zbl0475.46045
  19. [19] D.M. Topping: “On linear combinations of special operators”, J. Algebra, Vol. 10, (1968), pp. 516–521. http://dx.doi.org/10.1016/0021-8693(68)90077-X 
  20. [20] H. Upmeier: Symmetric Banach manifolds and Jordan C*-algebras, North Holland Mathematics Studies, Vol. 104, North-Holland Publishing Co., Amsterdam, 1985. Zbl0561.46032

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.