Abstract
Motivated by the well known Kadec-Pelczynski disjointifcation theorem, we undertake
an analysis of the supports of non-zero functions in strongly embedded subspaces of
Banach functions spaces. The main aim is to isolate those properties that bring additional
information on strongly embedded subspaces. This is the case of the support localization
property, which is a necessary condition fulflled by all strongly embedded subspaces. Several
examples that involve Rademacher functions, the Volterra operator, Lorentz spaces
or Orlicz spaces are provided.
