Limits of finite graphs, Von Neumann algebras and a Cheeger type inequality

Weak convergence of finite graphs, integrated density of states and a Cheeger type inequality

In [4] we proved that the limit of a weakly convergent sequence of finite graphs can be viewed as a graphing or a continuous field of infinite graphs. Thus one can associate a type II1-von Neumann algebra to such graph sequences. We show that in this case the integrated density of states exists that is the weak limit of the spectra of the graph Laplacians of the finite graphs is the KNS-spectra...

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 ...

Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.

Calculating Different Topological Indices of Von Neumann Regular Graph of Z_(p^α )

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

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