Displaying 41 – 60 of 154

Showing per page

Haar null and non-dominating sets

Sławomir Solecki (2001)

Fundamenta Mathematicae

We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of ω ω . Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain...

Idempotent States and the Inner Linearity Property

Teodor Banica, Uwe Franz, Adam Skalski (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A → Mₙ(ℂ) is a finite-dimensional representation of a Hopf C*-algebra, we prove that the idempotent state associated to its Hopf image A' must be the convolution Cesàro limit of the linear functional φ = tr ∘ π. We then discuss some consequences of this result, notably to inner linearity questions.

Currently displaying 41 – 60 of 154