Abstract
Given a stationary Gaussian vector process, consider a Markovian splitting subspace X contained in the frame space which is either observable or constructible. Such an X will be called reduced . In this paper we show that a Markovian splitting subspace is minimal if and only if it is reduced. This was claimed in some earlier papers but there are nontrivial gaps in the proofs presented there. The proof is based on a lemma staling that all reduced X have quasi-equivalent structural functions. This property is also important in isomorphism theory for minimal splitting subspaces.
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