  The structure of $^{26}$O is currently being investigated on both theoretical
and experimental fronts. It is well established that it is unbound and the
resonance parameters are fairly well-known. The theoretical analysis may
involved two- and three-body interactions, as well as correlations with the
continuum spectrum of energy. In order to properly assess the structure of the
ground and excited states, it is imperative to include a large single particle
representation with the right asymptotic behavior. The purpose of this work is
to provide details of the single particle continuum configurations of the
ground and excited $0^+$ states. We use a large complex energy single particle
basis, formed by resonances and complex energy scattering states, the so called
Berggren basis, and a separable interaction, which is convenient to solve in a
large model space. Three $0^+$ states were found in the complex energy plane.
Changes of the resonant parameters, i.e. energy and width, were analyzed as a
function of strength of the residual interaction. It is shown how a subtle
difference in the interaction could change the unbound character of $^{26}$O
into a Borromean nucleus. Only one of the two excited states can be considered
as a candidate for a physical meaningful resonance. The calculated occupation
probabilities are in agreement with other theoretical approaches although the
calculated half live is three-order of magnitude smaller than the experimental
one.
