A characterization of dual $B^{\ast }$-algebras
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- by Edith A. McCharen
- Proc. Amer. Math. Soc. 37 (1973), 84
- DOI: https://doi.org/10.1090/S0002-9939-1973-0306927-7
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Abstract:
Let A be a ${B^\ast }$-algebra. The second conjugate space of A, denoted by ${A^{ \ast \ast }}$, is a ${B^\ast }$-algebra under the Arens multiplication. A new proof is given that A is a dual algebra if and only if the natural image of A in ${A^{ \ast \ast }}$ is an ideal in ${A^{\ast \ast }}$.References
- B. J. Tomiuk and Pak-ken Wong, The Arens product and duality in $B^{\ast }$-algebras, Proc. Amer. Math. Soc. 25 (1970), 529–535. MR 259620, DOI 10.1090/S0002-9939-1970-0259620-0
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques [Scientific Reports], Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition. MR 246136
- R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York-Toronto-London, 1965. MR 221256
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 84
- MSC: Primary 46K05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0306927-7
- MathSciNet review: 0306927