We generalise the Riesz representation theorems for positive linear functionals on $$\text {C}_{\text {c}}(X)$$ and {0}}(X)$$ , where X is a locally compact Hausdorff space, to operators from these spaces into partially ordered vector space E. The representing measures are defined Borel $$\sigma $$ -algebra of take their values in extended cone corresponding integrals order integrals. give expl...

Section 2.1 below contains a brief introduction to the theory of C -algebras associated to graphs. Some examples are presented. Section 3 contains a discussion on stability of C -algebras. We make a digression to show that for any C -dynamical system (G; ;A) with G second countable, A separable and stable, the crossed product C -algebra A o G is stable. This generalizes [12, Corollary 4.5]. Sub...

For self-orthogonal modules T , the quotient triangulated categories D(A)/K(addT ) are studied, in particular, their relations with the stable categories of some Frobenius categories are investigated. New descriptions of the singularity categories of Gorenstein algebras are obtained; and the derived categories of Gorenstein algebras are explicitly given, inside the stable categories of the grad...

In this paper we show that stable rank of the C -algebras of simply connected, amenable Lie groups of type I is estimated by complex dimension of the spaces of all characters of these groups. It is extended to the connected case, by which we show that product formula of stable rank holds for the group C -algebras of connected, amenable Lie groups of type I. For further estimation of stable rank...