  Morrey (function) spaces and, in particular, smoothness spaces of
Besov-Morrey or Triebel-Lizorkin-Morrey type enjoyed a lot of interest
recently. Here we turn our attention to Morrey sequence spaces
$m_{u,p}=m_{u,p}(\mathbb{Z}^d)$, $0<p\leq u<\infty$, which have yet been
considered almost nowhere. They are defined as natural generalizations of the
classical $\ell_p$ spaces. We consider some basic features, embedding
properties, the pre-dual, a corresponding version of Pitt's compactness
theorem, and can further characterize the compactness of embeddings of related
finite-dimensional spaces.
