  If a body of dielectric material is coated by a plasmonic structure of
negative dielectric constant with nonzero loss parameter, then cloaking by
anomalous localized resonance (CALR) may occur as the loss parameter tends to
zero. The aim of this paper is to investigate this phenomenon in two and three
dimensions when the coated structure is radial, and the core, shell and matrix
are isotropic materials. In two dimensions, we show that if the real part of
the permittivity of the shell is -1 (under the assumption that the permittivity
of the background is 1), then CALR takes place. If it is different from -1,
then CALR does not occur. In three dimensions, we show that CALR does not
occur. The analysis of this paper reveals that occurrence of CALR is determined
by the eigenvalue distribution of the Neumann-Poincar\'e-type operator
associated with the structure.
