# Cut norm discontinuity of triangular truncation of graphons

@inproceedings{Mishura2021CutND, title={Cut norm discontinuity of triangular truncation of graphons}, author={Teddy Mishura}, year={2021} }

The space of L graphons, symmetric measurable functions w : [0, 1] → R with finite p-norm, features heavily in the study of sparse graph limit theory. We show that the triangular cut operator Mχ acting on this space is not continuous with respect to the cut norm. This is achieved by showing that as n→∞, the norm of the triangular truncation operator Tn on symmetric matrices equipped with the cut norm grows to infinity as well. Due to the density of symmetric matrices in the space of L graphons…

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