  We explicitly establish a unitary correspondence between spherical
irreducible tensor operators and cartesian tensor operators of any rank. That
unitary relation is implemented by means of a basis of integer-spin wave
functions that constitute simultaneously a basis of the spaces of cartesian and
spherical irreducible tensors. As a consequence, we extend the Wigner--Eckart
theorem to cartesian irreducible tensor operators of any rank, and to totally
symmetric reducible ones. We also discuss the tensorial structure of several
standard spherical irreducible tensors such as ordinary, bipolar and tensor
spherical harmonics, spin-polarization operators and multipole operators. As an
application, we obtain an explicit expression for the derivatives of any order
of spherical harmonics in terms of tensor spherical harmonics.
