Coboundary operators for infinite frameworks

Kastis, Eleftherios and Kitson, Derek and Power, Stephen (2019) Coboundary operators for infinite frameworks. Mathematical Proceedings of the Royal Irish Academy, 119A (2). pp. 93-110. ISSN 1393-7197

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Abstract

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?