Locally Solid Vector Lattices with the AM-Property

Let X be a locally solid vector lattice. We say that X possesses the AM-property provided that for every bounded set B X, the set of all nite suprema of elements of B, denoted by B_, is also bounded. This notion extends some properties regarding AM-spaces in Banach lattices to the category of all locally solid vector lattices. With the aid of this concept, we investigate some topological and ordered structures for the spaces of all bounded order bounded operators between locally solid vector lattices.