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

Bakonyi, Mihály

doi:10.1090/S0002-9939-01-06288-8

The extension of positive definite operator-valued functions defined on a symmetric interval of an ordered group
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Proc. Amer. Math. Soc. 130 (2002), 1401-1406 Request permission

Abstract:

Let $G_1$ be an ordered abelian group and $a\in G_1$. Let $G_2$ be an abelian group and $f$ an operator-valued positive definite function on $(-a,a)\times G_2$. We prove that $f$ admits a positive definite extension to $G_1\times G_2$, generalizing in this way existing results for the case when $G_1=\mathbf {R}$ and $f$ is continuous.

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