arXiv subjects

Fehmi Ekin Giritlioglu

Publications and source records attributed to Fehmi Ekin Giritlioglu.

2 recordsLinked to original sources

arXiv2026

Irreducibility and weak spectral gap in free product von Neumann algebras

Consider a free product $(M,φ)= (M_1,φ_1)* (M_2,φ_2)$ of non-trivial von Neumann algebras. Using amalgamated free product techniques, we establish irreducibility and weak spectral gap results for free product subalgebras and the centralizer subalgebra of the free product state. In particular, it is shown that, under a mild dimension constraint, the inclusion of the diffuse summand of these subalgebras into the corresponding corner of $M^ω$ is irreducible for any free ultrafilter $ω\in β\mathbb{N}\setminus \mathbb{N}$. We also obtain analogous irreducibility results for graph products of von Neumann algebras.

math.OA↗

arXiv2026

Translation Actions on Non-Unimodular Groups and Strong Ergodicity

We investigate translation actions of countable dense subgroups of non-unimodular locally compact second countable (lcsc) groups. Using left-right actions, we show that the left translation action $Γ\curvearrowright G$ given by a countable dense subgroup $Γ$ of a locally compact second countable group $G$ can only be strongly ergodic if $G$ is almost unimodular. We show that the strong ergodicity of the action $Γ\curvearrowright G$ for an almost unimodular lcsc group $G$ is equivalent to the strong ergodicity of $Γ\cap \ker(Δ_G)\curvearrowright \ker(Δ_G)$, where $Δ_G$ is the modular function. We demonstrate the absence of rigidity, by showing that non-isomorphic lcsc almost unimodular groups can admit orbit equivalent translation actions.

math.DS↗