On the multiplicity function of ergodic group extensions, II

Jakub Kwiatkowski; Mariusz Lemańczyk

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We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation $S T = T^{- 1} S$ . In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of $S^{2}$ . In particular, $S^{2}$ has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace $f \in L^{2} (X, ℱ, μ) : f (T^{2} x) = f (x)$ . For S and T ergodic satisfying this equation further constraints...

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Displaying similar documents to “On the multiplicity function of ergodic group extensions, II”

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Conjugacies between ergodic transformations and their inverses

Evolutionary Design of Digital Circuits Using Improved Multi Expression Programming (IMEP).

Theoretical and Practical Analysis about Census by Internet.

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Toeplitz $Z_{2}$ -extensions