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Coboundary operators for infinite frameworks

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<mark>Journal publication date</mark>4/11/2019
<mark>Journal</mark>Mathematical Proceedings of the Royal Irish Academy
Issue number2
Number of pages18
Pages (from-to)93-110
Publication StatusPublished
<mark>Original language</mark>English


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?