Topological dynamics of groupoid actions

Groupoid Actions on Fractafolds

We define a bundle over a totally disconnected set such that each fiber is homeomorphic to a fractal blowup. We prove that there is a natural action of a Renault–Deaconu groupoid on our fractafold bundle and that the resulting action groupoid is a Renault– Deaconu groupoid itself. We also show that when the bundle is locally compact the associated C∗-algebra is primitive and has a densely defin...

Topological Groupoid Quantales

We associate a canonical unital involutive quantale to a topological groupoid. When the groupoid is also étale, this association is compatible with but independent from the theory of localic étale groupoids and their quantales [19] of P. Resende. As a motivating example, we describe the connection between the quantale and the C∗-algebra that both classify Penrose tilings, which was left as an o...

On the topological centers of module actions

In this paper, we  study the Arens regularity properties of module actions. We investigate some properties of topological centers of module actions ${Z}^ell_{B^{**}}(A^{**})$ and  ${Z}^ell_{A^{**}}(B^{**})$ with some conclusions in group algebras.

Topological Centers of Certain Banach Module Actions

Topological centers of the n-th dual of module actions

We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let   $mathcal{B}$   be a Banach  $mathcal{A}-bimodule$. By using some new conditions, we show that $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and $ Z^ell_{mathcal{B}...