Unimodular eigenvalues and linear chaos in Hilbert spaces

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For linear operatorsT in a complex separable Hilbert spaceH we consider the problem of existence of invariant Gaussian measuresm:mT −1=m. We relate the size of the unimodular point spectrum ofT to mixing properties of the measure preserving transformations defined byT with respect to such invariant measures, and we draw some conclusions concerning orbit structure properties ofT.

The research for this work has been supported by a grant from the Research Center (KoE) of the Athens University of Economics and Business.