K-property for Maharam extensions of nonsingular Bernoulli and Markov\n shifts

2016/11/16 by Alexandre I. Danilenko, Mariusz Lemańczyk, Danilenko, Alexandre +1
Mathematics · #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.1611.05173

Abstract

It is shown that each conservative nonsingular Bernoulli shift is either of\ntype II₁ or III₁. Moreover, in the latter case the corresponding Maharam\nextension of the shift is a K-automorphism. This extends earlier results\nobtained by Z.~Kosloff for the equilibrial shifts. Nonequilibrial shifts of\ntype III₁ are constructed. We further generalize (partly) the main results\nto nonsingular Markov shifts.\n

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