Rational weak mixing in infinite measure spaces

Infinite Measure Preserving Transformations with "mixing"

Mixing operators on spaces with weak topology

We prove that a continuous linear operator T on a topological vector space X with weak topology is mixing if and only if the dual operator T ′ has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space ω due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator T on ω, ...

$psi -$weak Contractions in Fuzzy Metric Spaces

In this paper, the notion of $psi -$weak contraction cite{Rhoades} isextended to fuzzy metric spaces. The existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. Our resultgeneralizes a result of Gregori and Sapena cite{Gregori}.

Transformations of measure on infinite-dimensional vector spaces∗

Measurable Rigidity of Actions on Infinite Measure Homogeneous Spaces, Ii

Theorem 1.1 (Shalom and Steger, [21]). Measurable isomorphisms between linear actions on R of abstractly isomorphic lattices in SL2(R) are algebraic. More precisely, if τ : Γ1 ∼= −→Γ2 is an isomorphism between two lattices in SL2(R) and T : R → R is a measure class preserving map with T (γx) = γT (x) for a.e. x ∈ R and all γ ∈ Γ1, then there exists A ∈ GL2(R) so that γ = AγA−1 for all γ ∈ Γ1 an...