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Continuity of derivations on Mal'cev H*-algebras

Published online by Cambridge University Press:  24 October 2008

Borut Zalar
Borut Zalar
Affiliation:
Institute of Mathematics, University of Ljubljana, Jadranska 21, 61000-Ljubljana, Yugoslavia
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Extract

A long time ago the concept of H*-algebra was introduced by Ambrose in [1] where the structure of complex associative H*-algebras was given. Since then this theory was extended to such classical types of non-associative algebras as alternative algebras (in [6]), Jordan algebras (in [5, 13, 14]), non-commutative Jordan algebras (in [5]), Lie algebras (in [3, 9, 10]) and Mal'cev algebras (in [2]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 455 - 459
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Ambrose, W.. Structure theorems for a special class of Banach algebras. Trans. Amer. Math. Soc. 57 (1945), 364–386.CrossRefGoogle Scholar
[2]Cabrera, M., Martinez, J. and Rodriguez, A.. Mal'cev H-algebras. Math. Proc. Cambridge Philos. Soc. 103 (1988), 463–471.CrossRefGoogle Scholar
[3]Cuenca, J. A., Garcia, A. and Martin, C.. Structure theory for L*-algebras. Math. Proc. Cambridge Philos. Soc. 107 (1990), 361–365.CrossRefGoogle Scholar
[4]Cuenca, J. A. and Rodriguez, A.. Isomorphisms of H*-algebras. Math. Proc. Cambridge Philos. Soc. 97 (1985), 93–99.Google Scholar
[5]Cuenca, J. A. and Rodriguez, A.. Structure theory for noncommutative Jordan H*-algebras. J. Algebra 106 (1987), 1–14.Google Scholar
[6]de Guzman, I. P.. Structure theorems for alternative H*-algebras. Math. Proc. Cambridge Philos. Soc. 94 (1983), 437–446.CrossRefGoogle Scholar
[7]Rodriguez, A.. The uniqueness of complete norm topology in complete normed nonassociative algebras. J. Funct. Anal. 60 (1985), 1–15.Google Scholar
[8]Rodriguez, A.. Jordan axioms for C*-algebras. Manuscripta Math. 61 (1988), 297–314.CrossRefGoogle Scholar
[9]Schue, J. R.. Hilbert space methods in the theory of Lie algebras. Trans. Amer. Math. Soc. 95 (1960), 69–80.CrossRefGoogle Scholar
[10]Schue, J. R.. Cartan decompositions for L*-algebras. Trans. Amer. Math. Soc. 98 (1961), 334–349.Google Scholar
[11]Sinclair, A. M.. Automatic Continuity of Linear Operators (Cambridge University Press, 1976).CrossRefGoogle Scholar
[12]Sinclair, A. M. and Johnson, B. E.. Continuity of derivations and a problem of Kaplansky. Amer. J. Math. 90 (1968), 1067–1073.Google Scholar
[13]Viola, C.. Hilbert space methods in the theory of Jordan algebras. I. Proc. Cambridge Philos. Soc. 78 (1974), 292–300.Google Scholar
[14]Viola, C.. Hilbert space methods in the theory of Jordan algebras. II. Math. Proc. Cambridge Philos. Soc. 79 (1976), 307–319.Google Scholar
[15]Zalar, B.. On derivations of H*-algebras. Preprint (1991).Google Scholar