If following the hearing the legislative body shall determine that the pedestrian mall shall be established, and if at that time there remain any written claims for damages which have not been allowed pursuant to Section 11310 or which have not been withdrawn, the legislative body shall direct that an action or actions be brought in the superior court in the name of the city by the county counsel, district attorney, or city attorney, as the case may be, or other attorney designated by the legislative body for a determination of the damages, if any, to which the claimant may legally be entitled because of the establishment of the pedestrian mall. Such action shall be in the nature of a proceeding in eminent domain for the condemnation of the right or rights in real property, the taking of which by the establishment of the pedestrian mall results in the damages claimed. Except as may otherwise be provided in this part, such action and proceeding shall be governed so far as the same may be made applicable by the provisions relating to proceedings in eminent domain. Except as provided in Article 2 (commencing with Section 1245.210) of Chapter 4 of Title 7 of Part 3 of the Code of Civil Procedure, in any such action the resolution of intention adopted pursuant to this part and the resolution adopted under Section 11311 conclusively establish the matters referred to in Section 1240.030 of the Code of Civil Procedure.