  We prove that a vector bundle $\pi : E \to M$ is characterized by the Lie
algebra generated by all differential operators on $E$ which are eigenvectors
of the Lie derivative in the direction of the Euler vector field. Our result is
of Pursell-Shanks type but it is remarkable in the sense that it is the whole
fibration that is characterized here. The proof relies on a theorem of [Lecomte
P., J. Math. Pures Appl. (9) 60 (1981), 229-239] and inherits the same
hypotheses. In particular, our characterization holds only for vector bundles
of rank greater than 1.
