Zero product preserving linear maps of CCR C∗-algebras with Hausdorff spectrum

In this paper, we try to attack a conjecture of Araujo and Jarosz that every bijective linear map θ between C∗-algebras, with both θ and its inverse θ−1 preserving zero products, arises from an algebra isomorphism followed by a central multiplier. We show it is true for CCR C∗-algebras with Hausdorff spectrum, and in general, some special C∗-algebras associated to continuous fields of C∗-algebras.