Circular annihilators of logarithmic classes

Given a real abelian field F with group G and an odd prime number {\ell}, we define the circular subgroup of the pro-{\ell}-group of logarithmic units and we show that for any Galois morphism $\rho$ from the pro-{\ell}-group of logarithmic units to Z{\ell} [G ], the image of the circular subgroup annihilates the {\ell}-group of logarithmic classes. We deduce from this a proof of a logarithmic version of Solomon conjecture.