Proceedings of the American Mathematical Society · 1971 · 13 citations · 1 references
Natural SciencesMathematicsDynamical SystemsProbability TheoryStochastic ProcessesEntropyErgodic TheoryOperator TheorySpectral TheoryEntropy In Ergodic TheoryErgodic ProcessesErgodic PropertiesErgodic TransformationInvertible TransformationsMeasure-preserving TransformationMeasure-theoretic EntropyTransformations
A class of ergodic, measure-preserving, invertible point transformations is defined, called class 5. Any measurepreserving point transformation induces a unitary operator on the Hilbert space of 2-functions.A theorem is proved here which implies that the operator induced by any transformation in class 5 has simple spectrum.[It is then a known result that the transformations in class 5 have zero entropy.]
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