Coboundary operators for infinite frameworks

We consider, from the point of view of operator theory, a class of infinite matrices in which the matrix entries are determined by an underlying graph structure with accompanying geometric data. This class includes the rigidity matrices of infinite bar-joint frameworks, as well as the incidence matrices of infinite directed graphs. We consider the following questions: When do these matrices give rise to bounded operators? Can we compute the operator norm? When are these operators compact? And when are they bounded below? CC BY 4.0—This work is licensed under the Creative Commons Attribution 2.0 Generic License. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/legalcode