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Hilbert space methods in the theory of Jordan algebras. I

Published online by Cambridge University Press:  24 October 2008

C. Viola Devapakkiam
C. Viola Devapakkiam
Affiliation:
The Ramanujan Institute, University of Madras, Madras 5 (India)
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Extract

In this paper, we study the structure of certain infinite-dimensional Jordan algebras admitting an inner product. These algebras, called J*-algebras in the sequel, have already been considered in (4) in connexion with the norm uniqueness problem for non-associative algebras. We deal here with the structure and classification of these algebras. Existence of self-adjoint idempotents plays a central role in the classification problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 2 , September 1975 , pp. 293 - 300
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Albert, A. A.On Jordan algebras of linear transformations. Trans. Amer. Math. Soc. 59 (1946), 524–555.CrossRefGoogle Scholar
(2)Albert, A. A.A structure theory for Jordan algebras. Ann. of Math. (2) 48 (1947), 546–567.CrossRefGoogle Scholar
(3)Ambrose, W.Structure theorem for a special class of Banach algebras. Trans. Amer. Math. Soc. 57 (1945), 364–386.CrossRefGoogle Scholar
(4)Balachandran, V. K. and Rema, P. S.Uniqueness of norm topology in certain Banach Jordan algebras, Publications of the Ramanujan Institute No. 1 (1969), 283–289.Google Scholar
(5)Hel, Braun and Koecher, M.Jordan Algebren Bd. 128, Springer, 1966.Google Scholar
(6)Jacobson, N.Structure and Representation Jordan Algebras. Amer. Math. Soc. Colloq. Pub. XXXIV (1968).Google Scholar
(7)Naimark, M. A.Normed Rings, P. Noordhoff N. V. The Netherlands (1959).Google Scholar
(8)Schue, J. R.Hilbert Space Methods in the theory of Lie algebras. Trans. Amer. Math. Soc. 95 (1960), 69–80.CrossRefGoogle Scholar
(9)Viola, Devapakkiam C.Jordan algebras with continuous inverse. Mathematics Japonicae 16 (1971).Google Scholar
(10)Viola, Devapakkiam C. Banach Jordan Algebras, Doctoral Dissertation, University of Madras, 1970.Google Scholar