Banach space actions and L2-spectral gap

Limit theorems for stationary Markov processes with L2-spectral gap

Let (Xt, Yt)t∈T be a discrete or continuous-time Markov process with state space X × R where X is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. (Xt, Yt)t∈T is assumed to be a Markov additive process. In particular, this implies that the first component (Xt)t∈T is also a Markov process. Markov random walks or additive f...

Arens regularity of bilinear maps and Banach modules actions

‎Let $X$‎, ‎$Y$ and $Z$ be Banach spaces and $f:Xtimes Y‎ ‎longrightarrow Z$ a bounded bilinear map‎. ‎In this paper we‎ ‎study the relation between Arens regularity of $f$ and the‎ ‎reflexivity of $Y$‎. ‎We also give some conditions under which the‎ ‎Arens regularity of a Banach algebra $A$ implies the Arens‎ ‎regularity of certain Banach right module action of $A$‎ .

Topological Centers of Certain Banach Module Actions

COCYCLE SUPERRIGIDITY FOR MALLEABLE ACTIONS WITH SPECTRAL GAP Preliminary version

Let Γ y X be a measure preserving (m.p.) action of a discrete group Γ on a probability measure space (X,μ) and H ⊂ Γ a non-amenable subgroup with commutant H = {g ∈ Γ | gh = hg, ∀h ∈ H} infinite. We prove that if the action satisfies a malleability condition on HH, is weak mixing on H and has stable spectral gap on H (e.g. if the action is Bernoulli on HH), then any cocycle with values in a Pol...

On the Superrigidity of Malleable Actions with Spectral Gap

We prove that if a countable group Γ contains a non-amenable subgroup with centralizer infinite and “weakly normal” in Γ (e.g. if Γ is non-amenable and has infinite center or is a product of infinite groups) then any measure preserving Γ-action on a probability space which satisfies certain malleability, spectral gap and weak mixing conditions is cocycle superrigid. We also show that if Γ y X i...