Abstract
We consider, in this note, some invariant subspaces of a unitary operator induced by a measure preserving transformation. For these subspaces two problems are studied:
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a.
Is the subspace generated by characteristic functions?
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b.
When is an invariant subspace a reducing subspace?
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References
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This work was partially supported by N.S.F. Grant No. GP 2491.
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Foguel, S.R. Invariant subspaces of a measure preserving transformation. Israel J. Math. 2, 198–200 (1964). https://doi.org/10.1007/BF02759944
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DOI: https://doi.org/10.1007/BF02759944