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2 Colloquium Mathematicum

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On v-positive type transformations in infinite measure

100%

Pădurariu T. , Silva C. , Zachos E.

tom 140

nr 2

149-170

For each vector v we define the notion of a v-positive type for infinite-measure-preserving transformations, a refinement of positive type as introduced by Hajian and Kakutani. We prove that a positive type transformation need not be (1,2)-positive type. We study this notion in the context of Markov shifts and multiple recurrence, and give several examples.

Ergodicity and conservativity of products of infinite transformations and their inverses

75%

Clancy J. , Friedberg R. , Kasmalkar I. , Loh I. , Pădurariu T. , Silva C. , Vasudevan S.

nr 2

271-291

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation T in the class, the cartesian product T × T is ergodic, but the product $T × T^{-1}$ is not. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.