Annihilator ideals in the cohomology of Banach algebras
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- by A. M. Sinclair PDF
- Proc. Amer. Math. Soc. 33 (1972), 361-366 Request permission
Abstract:
If A is a ${C^\ast }$-algebra, if X is a Banach A-module, and if J is the annihilator of X in A, then the cohomology space ${\mathcal {H}^n}(A,{X^\ast })$ is isomorphic to ${\mathcal {H}^n}(A/J,{X^\ast })$ for each positive integer n.References
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- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- G. Hochschild, On the cohomology groups of an associative algebra, Ann. of Math. (2) 46 (1945), 58–67. MR 11076, DOI 10.2307/1969145
- B. E. Johnson, The Wedderburn decomposition of Banach algebras with finite dimensional radical, Amer. J. Math. 90 (1968), 866–876. MR 233206, DOI 10.2307/2373486 —, Cohomology in Banach algebras, Mem. Amer. Math. Soc. (to appear).
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 361-366
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0295096-7
- MathSciNet review: 0295096