# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 35 (2006) pp.601-611

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### Abstract

In this note, we study invariant subspaces of $L^2(\Bbb T^2)$ with respect to certain von Neumann algebras. We give a characterization of Beurling-type left-invariant subspaces of $L^2(\Bbb T^2)$. We also give a structure theorem of a non-trivial two-sided invariant subspace of $L^2(\Bbb T^2)$.

MSC(Primary) 46L10 47A15 von Neumann algebras, invariant subspaces, Popovici's decomposition