A note on two-sided ideals in $C^*$-algebras
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- by John Bunce PDF
- Proc. Amer. Math. Soc. 28 (1971), 635 Request permission
Abstract:
An elementary proof is given of the fact that ${(I + J)^ + } = {I^ + } + {J^ + }$ for $I$ and $J$ closed two-sided ideals in a ${C^ \ast }$-algebra.References
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Edward G. Effros, Order ideals in a $C^{\ast }$-algebra and its dual, Duke Math. J. 30 (1963), 391–411. MR 151864
- Gert Kjaergȧrd Pedersen, A decomposition theorem for $C^{\ast }$ algebras, Math. Scand. 22 (1969), 266–268 (1969). MR 253062, DOI 10.7146/math.scand.a-10890
- Erling Størmer, Two-sided ideals in $C^{\ast }$-algebras, Bull. Amer. Math. Soc. 73 (1967), 254–257. MR 208400, DOI 10.1090/S0002-9904-1967-11705-1
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 635
- MSC: Primary 46.65
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276780-7
- MathSciNet review: 0276780