  The structure of dynamically generated states in the chiral unitary approach
is studied from a viewpoint of their compositeness. We analyze the properties
of bound states, virtual states, and resonances in a single-channel chiral
unitary approach, paying attention to the energy dependence of the chiral
interaction. We define the compositeness of a bound state using the field
renormalization constant which is given by the overlap of the bare state and
the physical state in the nonrelativistic quantum mechanics, or by the residue
of the bound state propagator in the relativistic field theory. The field
renormalization constant enables one to define a normalized quantitative
measure of compositeness of the bound state. Applying this scheme to the chiral
unitary approach, we find that the bound state generated by the
energy-independent interaction is always a purely composite particle, while the
energy-dependent chiral interaction introduces the elementary component,
depending on the value of the cutoff parameter. This feature agrees with the
analysis of the effective interaction by changing the cutoff parameter. A
purely composite bound state can be realized by the chiral interaction only
when the bound state lies at the threshold or when the strength of the two-body
attractive interaction is infinitely large. The natural renormalization scheme,
introduced by the property of the loop function and the matching with the
chiral low-energy theorem, is shown to generate a bound state which is
dominated by the composite structure when the binding energy is small.
