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Let G 1 be an ordered abelian group and a E G 1 . Let G 2 be an abelian group and f an operator-valued positive definite function on (-a, a) x G 2 . We prove that f admits a positive definite extension to G 1 x G 2 , generalizing in this way existing results for the case when G 1 = R and f is continuous.

The extension of positive definite operator-valued functions defined on a symmetric interval of an ordered group