# The continuity of Lie homomorphisms

Bernard Aupetit; Martin Mathieu

Studia Mathematica (2000)

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

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topAupetit, 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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- [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] 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] V. Pták, Derivations, commutators and the radical, Manuscripta Math. 23 (1978), 355-362. Zbl0376.46031
- [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] P. Šemrl, Spectrally bounded linear maps on B(H), Quart. J. Math. Oxford (2) 49 (1998), 87-92. Zbl0958.47016

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