In applications, it happens often that one wants to study convergence of operators such as Laplacians on spaces that change as well. A prominent example is the convergence of Laplacians on thick graphs (e.g. open subsets shrinking to a metric graph) towards the standard Laplacian on a metric graph. Classical convergence assumes that the operators are defined on the same space.
In this talk we discuss two apparently different concepts of convergence of the resolvents in operator norm; both named ``generalised norm resolvent convergence'': the first developed by Weidmann, the second developed independently based on the so-called ``quasi-unitary equivalence''. Surprisingly, not only the given names are the same, but both concepts are (almost) equivalent. We illustrate the ideas with many examples.