Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-30T21:02:22.380Z Has data issue: false hasContentIssue false

Continuity of derivations on Mal'cev H*-algebras

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ambrose, W.. Structure theorems for a special class of Banach algebras. Trans. Amer. Math. Soc. 57 (1945), 364386.CrossRefGoogle Scholar
[2]Cabrera, M., Martinez, J. and Rodriguez, A.. Mal'cev H-algebras. Math. Proc. Cambridge Philos. Soc. 103 (1988), 463471.CrossRefGoogle Scholar
[3]Cuenca, J. A., Garcia, A. and Martin, C.. Structure theory for L*-algebras. Math. Proc. Cambridge Philos. Soc. 107 (1990), 361365.CrossRefGoogle Scholar
[4]Cuenca, J. A. and Rodriguez, A.. Isomorphisms of H*-algebras. Math. Proc. Cambridge Philos. Soc. 97 (1985), 9399.Google Scholar
[5]Cuenca, J. A. and Rodriguez, A.. Structure theory for noncommutative Jordan H*-algebras. J. Algebra 106 (1987), 114.Google Scholar
[6]de Guzman, I. P.. Structure theorems for alternative H*-algebras. Math. Proc. Cambridge Philos. Soc. 94 (1983), 437446.CrossRefGoogle Scholar
[7]Rodriguez, A.. The uniqueness of complete norm topology in complete normed nonassociative algebras. J. Funct. Anal. 60 (1985), 115.Google Scholar
[8]Rodriguez, A.. Jordan axioms for C*-algebras. Manuscripta Math. 61 (1988), 297314.CrossRefGoogle Scholar
[9]Schue, J. R.. Hilbert space methods in the theory of Lie algebras. Trans. Amer. Math. Soc. 95 (1960), 6980.CrossRefGoogle Scholar
[10]Schue, J. R.. Cartan decompositions for L*-algebras. Trans. Amer. Math. Soc. 98 (1961), 334349.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), 10671073.Google Scholar
[13]Viola, C.. Hilbert space methods in the theory of Jordan algebras. I. Proc. Cambridge Philos. Soc. 78 (1974), 292300.Google Scholar
[14]Viola, C.. Hilbert space methods in the theory of Jordan algebras. II. Math. Proc. Cambridge Philos. Soc. 79 (1976), 307319.Google Scholar
[15]Zalar, B.. On derivations of H*-algebras. Preprint (1991).Google Scholar