  Bound, antibound and resonance states are associated to poles in the on-shell
partial wave amplitudes. We show here that from the residues of the pole a rank
1 projection operator associated with any of these states can be extracted, in
terms of which a sum rule related to the composition of the state can be
derived. Although typically it involves complex coefficients for the
compositeness and elementariness, except for the bound state case, we
demonstrate that one can formulate a meaningful compositeness relation with
only positive coefficients for resonances whose associated Laurent series in
the variable s converges in a region of the physical axis around Re(s_P), with
s_P the pole position of the resonance. It is also shown that this result can
be considered as an analytical extrapolation in s_P of the clear narrow
resonance case. We exemplify this formalism to study the two-body components of
several resonances of interest.
