Abstract. We present some generalizations of quantum information inequalities involving tracial positive linear maps between C∗-algebras. Among several results, we establish a noncommutative Heisenberg uncertainty relation. More precisely, we show that if Φ : A → B is a tracial positive linear map between C∗-algebras , ρ ∈ A is a Φ-density element and A,B are self-adjoint operators of A such th...

Given an action of a compact group on complex vector bundle, there is induced the associated Cuntz--Pimsner algebra. We determine conditions under which this has finite Rokhlin dimension.

We consider the reduction of problems on general noncommutative Lp-spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is an unpublished result of the first-named author which approximates any noncommutative Lpspace by tracial ones. We show that under some natural conditions a map between two von Neumann algebras extends to their crossed products...

It is a natural consequence of fundamental properties of the Casson invariant that the Rokhlin invariant μ(M) of an amphichiral integral homology 3–sphere M vanishes. In this paper, we give a new direct proof of this vanishing property. For such an M , we construct a manifold pair (Y,Q) of dimensions 6 and 3 equipped with some additional structure (6–dimensional spin e-manifold), such that Q ∼=...

Abstract In this paper, we study connections between positive entropy phenomena and the Koopman representation for actions of general countable groups. Following line work initiated by Hayes sofic entropy, show in a certain precise manner that all must come from portions embed into left-regular representation. We conclude having completely outer be isomorphic to direct sum This generalizes theo...

We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Frøyshov’s correction term in this setting is an integer-valued invariant of homology cobordism whose mod 2 reduction is the Rokhlin invariant. As an application, we show that there are no homology 3-spheres Y of Rokhlin invariant one such that Y #Y bounds a...