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Let X be a compact Hausdorff space and A a Banach algebra. We investigate amenability properties of the algebra C(X, A) of all A-valued continuous functions. We show that C(X, A) has a bounded approximate diagonal if and only if A has a bounded approximate diagonal; if A has a compactly central approximate diagonal (unbounded) then C(X, A) has a compactly approximate diagonal. Weak amenability of C(X, A) for commutative A is also considered.

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