I've been trying to understand a construction in the paper "Degree Growth of Meromorphic Surface Maps" by Bouksom, Favre and Jonsson. In it they state,
In fact, the completion can be characterized by the following universal property: if $(Y, q)$ is a complete topological vector space with a continuous nondegenerate quadratic form of Minkowski type, any isometry $T : C(X) → Y$ continuously extends to $L^2(X) → Y$ .
I don't know what a quadratic form of Minkowski type on an infinite dimensional vector space is. I was wondering if anyone knew of a reference for this?
