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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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