Abelian subalgebras of von Neumann algebras from flat tori in locally symmetric spaces

Abelian Subalgebras of Von Neumann Algebras from Flat Tori in Locally Symmetric Spaces

Consider a compact locally symmetric space M of rank r, with fundamental group Γ. The von Neumann algebra VN(Γ) is the convolution algebra of functions f ∈ l2(Γ) which act by left convolution on l2(Γ). Let T r be a totally geodesic flat torus of dimension r in M and let Γ0 ∼= Z r be the image of the fundamental group of T r in Γ. Then VN(Γ0) is a maximal abelian ⋆-subalgebra of VN(Γ) and its un...

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

reiter’s properties for the actions of locally compact quantum goups on von neumann algebras

von Neumann Algebras

For every selfadjoint operator T in the Hilbert space H, f(T) makes sense not only in the obvious case where / is a polynomial but also if / is just measurable, and if fn(x)-+f(x) for all x£R (with (/,) bounded) then fn(T)-+f(T) weakly, i.e. <fn(T)£9i)+<f(T)£9ti)V£9fiCH. Moreover the set {f(T)9 f measurable} is the set of all operators S in H invariant under all unitary transformations of H whi...