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Orthogonal decompositions in Hilbert \(C^*\)-modules and stationary processes. (English) Zbl 0927.46031
Summary: It is obtained a Wold-type decomposition for an adjointable isometry on a Hilbert \(C^*\)-module which is sequentially complete with respect to some locally convex topology, denoted by \(s\). Particularly self-dual Hilbert \(C^*\)-modules satisfy this condition. Finally, as an application we give a new proof of the Wold decomposition theorem for discrete stationary processes in complete correlated actions.

MSC:
46L08 \(C^*\)-modules
46L10 General theory of von Neumann algebras
60G15 Gaussian processes
46L45 Decomposition theory for \(C^*\)-algebras
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