We prove that the von Neumann algebras generated by n q-Gaussian elements, are factors for n > 2.

We prove a von Neumann type ergodic theorem for averages of unitary operators arising from the Furstenberg-Poisson boundary representation (the quasi-regular representation) of any lattice in a non-compact connected semisimple Lie group with finite center.

λ(s)δt = δst and ρ(s)δt = δts−1 for s, t ∈ Γ. The reduced group C∗-algebra C∗ λΓ is the C∗-algebra generated by λ, likewise for C∗ ρΓ; C∗ λΓ = λ(CΓ) ‖ ‖ ⊂ B(`2Γ) and C∗ ρΓ = ρ(CΓ) ‖ ‖ ⊂ B(`2Γ). The group von Neumann algebra LΓ is the von Neumann algebra generated by λ; LΓ = λ(CΓ)′′ = ρ(CΓ)′. We sometime use M instead of LΓ, and L2M instead of `2Γ. We denote by τ the canonical tracial state on L...

Zusammenfassung Es wurden zwei empirische Studien durchgeführt. In der einen Studie konnten Internetnutzer ihr Suchverhalten aus ihrer Sicht in einer Online Umfrage beschreiben. Die Fragen orientieren sich an den Ergebnissen früherer Studien und sind durch neue Fragestellungen bei der Online Suche erweitert worden. In der anderen Studie wurden vier weltweit Datensätze von Suchanfragen generiert...

viii

We prove that certain classes of von Neumann algebras with regular, injective subalgebras are thin. As a consequence, all Hochschild cohomology groups of these algebras are zero. Mathematics subject classification (2010): 46L10, 47A16.

We consider the class of all commutative reduced rings for which there exists a finite subset T ⊂ A such that all projections on quotients by prime ideals of A are surjective when restricted to T . A complete structure theorem is given for this class of rings, and it is studied its relation with other finiteness conditions on the quotients of a ring over its prime ideals. Introduction Our aim i...

Let T be a triangular ring. An additive map δ from T into itself is said to be Jordan derivable at an element Z ∈ T if δ(A)B +Aδ(B) + δ(B)A+Bδ(A) = δ(AB+BA) for any A,B ∈ T with AB + BA = Z. An element Z ∈ T is called a Jordan all-derivable point of T if every additive map Jordan derivable at Z is a Jordan derivation. In this paper, we show that some idempotents in T are Jordan all-derivable po...

form the base of a topology on the Stone spectrum Q(R) such that Q(R) becomes a zero-dimensional, completely regular Hausdorff space. The sets QP (R) are closed-open. If the von Neumann algebra R is abelian, then the Stone spectrum Q(R) is homeomorphic to the Gelfand spectrum Ω(R) of R. For an arbitrary non-abelian unital von Neumann algebra R, the Stone spectrum can hence be regarded as a non-...