  Kernel theorems, in general, provide a convenient representation of bounded
linear operators. For the operator acting on a concrete function space, this
means that its action on any element of the space can be expressed as a
generalised integral operator, in a way reminiscent of the matrix
representation of linear operators acting on finite dimensional vector spaces.
We prove kernel theorems for bounded linear operators acting on co-orbit spaces
associated with localised frames. Our two main results consist in
characterising the spaces of operators whose generalised integral kernels
belong to the co-orbit spaces of test functions and distributions associated
with the tensor product of the localised frames respectively. Moreover, using a
version of Schur's test, we establish a characterisation of the bounded linear
operators between some specific co-orbit spaces.
