  We extend our previous work on the electromagnetic Casimir-Lifshitz
interaction between two bodies when one is contained within the other. We focus
on the fluctuation-induced pressure acting on the cavity wall, which is assumed
to be spherical. This pressure can be positive or negative depending on the
response functions describing the bodies and the medium filling the cavity.
However, we find that, under general hypotheses, the sign is independent of the
geometry of the configuration. This result is based on the representation of
the Casimir-Lifshitz energy in terms of transition operators. In particular, we
study the components of these operators related to inside scattering
amplitudes, adapting the invariant imbedding procedure to this unfamiliar
scattering setup. We find that our main result is in agreement with the
Dzyaloshinskii-Lifshitz-Pitaevskii result, which is obtained as a limiting
case.
