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We show that the continuous cohomology groups of a $ p $-adic reductive groupwith coefficients in the locally analytic vectors of an admissible $\mathbb{Q}_p $-Banach space representation are homeomorphic to those withcoefficients in the Banach space representation itself. Moreover, we deducethat the canonical topologies on those continuous cohomology groups areHausdorff and are the uniquely determined finest locally convex topologies.

Continuous group cohomology with coefficients in locally analytic vectors of admissible $ \mathbb{Q}_p $-Banach space representations