Abstract
If A is a C ∗ {C^\ast } -algebra, if X is a Banach A-module, and if J is the annihilator of X in A, then the cohomology space H n ( A , X ∗ ) {\mathcal {H}^n}(A,{X^\ast }) is isomorphic to H n ( A / J , X ∗ ) {\mathcal {H}^n}(A/J,{X^\ast }) for each positive integer n.
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