  Low-rank tensor approximation techniques attempt to mitigate the overwhelming
complexity of linear algebra tasks arising from high-dimensional applications.
In this work, we study the low-rank approximability of solutions to linear
systems and eigenvalue problems on Hilbert spaces. Although this question is
central to the success of all existing solvers based on low-rank tensor
techniques, very few of the results available so far allow to draw meaningful
conclusions for higher dimensions. In this work, we develop a constructive
framework to study low-rank approximability. One major assumption is that the
involved linear operator admits a low-rank representation with respect to the
chosen tensor format, a property that is known to hold in a number of
applications. Simple conditions, which are shown to hold for a fairly general
problem class, guarantee that our derived low-rank truncation error estimates
do not deteriorate as the dimensionality increases.
