  The tomographic description of a quantum state is formulated in an abstract
infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt
linear operators, with trace formula as scalar product. Resolutions of the
unity, written in terms of over-complete sets of rank-one projectors and of
associated Gram-Schmidt operators taking into account their non-orthogonality,
are then used to reconstruct a quantum state from its tomograms. Examples of
well known tomographic descriptions illustrate the exposed theory.
