Abstract

We study actions of the Vilenkin group ∏∞k=0ℤm(k) onLp-spaces associated with a semi-finite von Neumann algebra М, via a generalized triangular truncation operator. The systems of eigenspaces that arise contain the classical unbounded Vilenkin systems and we show that such systems with the inverse lexicographic enumeration form Schauder decompositions in all reflexive non-commutativeLp-spaces. This is a non-commutative analogue of a theorem of Paley for unbounded Vilenkin systems, which in the classical setting is due to W.S. Young, F. Schipp and P. Simon.

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