The continuity of Lie homomorphisms

Bernard Aupetit; Martin Mathieu

Studia Mathematica (2000)

  • Volume: 138, Issue: 2, page 193-199
  • ISSN: 0039-3223

Abstract

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We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.

How to cite

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Aupetit, Bernard, and Mathieu, Martin. "The continuity of Lie homomorphisms." Studia Mathematica 138.2 (2000): 193-199. <http://eudml.org/doc/216698>.

@article{Aupetit2000,
abstract = {We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.},
author = {Aupetit, Bernard, Mathieu, Martin},
journal = {Studia Mathematica},
keywords = {Lie homomorphisms; Banach algebras; spectrally bounded maps; separating space; Lie homomorphism; centre modulo radical; surjectivity},
language = {eng},
number = {2},
pages = {193-199},
title = {The continuity of Lie homomorphisms},
url = {http://eudml.org/doc/216698},
volume = {138},
year = {2000},
}

TY - JOUR
AU - Aupetit, Bernard
AU - Mathieu, Martin
TI - The continuity of Lie homomorphisms
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 2
SP - 193
EP - 199
AB - We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.
LA - eng
KW - Lie homomorphisms; Banach algebras; spectrally bounded maps; separating space; Lie homomorphism; centre modulo radical; surjectivity
UR - http://eudml.org/doc/216698
ER -

References

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  2. [2] B. Aupetit, A Primer on Spectral Theory, Springer, New York, 1991. 
  3. [3] K. I. Beidar, W. S. Martindale and A. V. Mikhalev, Rings with Generalized Identities, Marcel Dekker, New York, 1996. Zbl0847.16001
  4. [4] M. I. Berenguer and A. R. Villena, Continuity of Lie isomorphisms of Banach algebras, Bull. London Math. Soc. 31 (1999), 6-10. Zbl1068.46500
  5. [5] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973. Zbl0271.46039
  6. [6] M. Brešar, Derivations decreasing the spectral radius, Arch. Math. (Basel) 61 (1993), 160-162. Zbl0818.46049
  7. [7] M. Brešar and M. Mathieu, Derivations mapping into the radical, III, J. Funct. Anal. 133 (1995), 21-29. Zbl0897.46045
  8. [8] M. Brešar and P. Šemrl, Spectral characterization of central elements in Banach algebras, Studia Math. 120 (1996), 47-52. 
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  10. [10] H. G. Dales, On norms of algebras, in: Proc. Centre Math. Anal. Austral. Nat. Univ. 21, Canberra, 1989, 61-96. 
  11. [11] M. Mathieu, Where to find the image of a derivation, in: Banach Center Publ. 30, Inst. Math., Polish Acad. Sci., Warszawa, 1994, 237-249. Zbl0813.47043
  12. [12] M. Mathieu, Lie mappings of C*-algebras, in: Nonassociative Algebra and Its Applications, R. Costa et al. (eds.), Marcel Dekker, New York, in press. 
  13. [13] V. Pták, Derivations, commutators and the radical, Manuscripta Math. 23 (1978), 355-362. Zbl0376.46031
  14. [14] A. Rodríguez Palacios, The uniqueness of the complete norm topology in complete normed nonassociative algebras, J. Funct. Anal. 60 (1985), 1-15. Zbl0602.46055
  15. [15] P. Šemrl, Spectrally bounded linear maps on B(H), Quart. J. Math. Oxford (2) 49 (1998), 87-92. Zbl0958.47016

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