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The Second Dual of a C*-Ternary Ring

Published online by Cambridge University Press:  20 November 2018

E. M. Landesman
Affiliation:
Department of Mathematics, University of California, Santa CruzCA 95064
Bernard Russo
Affiliation:
Department of Mathematics, University of California, IrvineCA 92717
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Abstract

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The Arens extension of the triple product of an associative triple system is studied. Using a representation theorem for C*-ternary rings due to Zettl, it is shown that the second dual of a C*-ternary ring is itself a C*-ternary ring

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Arens, R., Operations induced in function classes, Monat. für Math. 55 (1951) 119.Google Scholar
2. Bonsall, F. F. and Duncan, J., Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, Lon. Math. Soc. Lecture Note Series. 2, 1971.Google Scholar
3. Bonsall, F. F., Complete Normed Algebras, Springer-Verlag, 1973.Google Scholar
4. Dixmier, J., Les algebres d'operateurs dans Vaspace Hilbertien, Gauthier Villars, 1957, 2nd edition 1969.Google Scholar
5. Dixmier, J., Les C*-algebres et leurs representations, Gauthier Villars, 1964, 2nd edition 1969.Google Scholar
6. Friedman, Y. and Russo, B., Contractive projections on C0(K), Trans, A.M.S. 273 (1982) 5773.Google Scholar
7. Harris, L., Bounded symmetric homogeneous domains in infinite dimensional spaces, Lect. Notes in Math., No. 364, Springer (1973) 1340.Google Scholar
8. Hestenes, M. R., A ternary algebra with applications to matrices and linear transformations, Arch. Rat. Mech. An. 11 (1962) 138194.Google Scholar
9. Hestenes, M. R., Relative self adjoint operators in Hilbert space, Pac. J. Math. 11 (1961) 13151357.Google Scholar
10. Lister, W. G., Ternary rings, Trans. A.M.S. 154 (1971) 3755.Google Scholar
11. Loos, O., Assoziative Tripelsysteme, Manu. Math. 7 (1972) 103112.Google Scholar
12. Zettl, H. H., A characterization of ternary rings of operators, preprint, Saarbrucken, 1979.Google Scholar