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.
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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.