  A duality property for star products is exhibited. In view of it, known
star-product schemes, like the Weyl-Wigner-Moyal formalism, the Husimi and the
Glauber-Sudarshan maps are revisited and their dual partners elucidated. The
tomographic map, which has been recently described as yet another star product
scheme, is considered. It yields a noncommutative algebra of operator symbols
which are positive definite probability distributions. Through the duality
symmetry a new noncommutative algebra of operator symbols is found, equipped
with a new star product. The kernel of the new star product is established in
explicit form and examples are considered.
