Primary: - To assess progression-free survival rate at three months Secondary: - To determine the toxicity and safety of systemic infusion of anti-TGF beta antibody at three-week dosing intervals. - To assess time to progression and overall survival - to assess response rate using Modified RECIST Criteria for Mesothelioma Additional Objectives: - To assess efficacy using serial measurements of serum [and intrapleural, if indwelling catheter in place] biomarkers, including serum-mesothelin related peptide (SMRP/Mesomark®) and osteopontin. - To assess systemic [and intrapleural if indwelling catheter in place] humoral anti-tumor immune responses after repeated anti-TGF beta antibody instillation. - To assess systemic [and intrapleural, if indwelling catheter in place] TGF beta, and other cytokine levels after repeated anti-TGF beta antibody instillation. - To assess biologic response measurements of TGF beta blockade from serum tests and from pleural fluid or biopsy tissue if this is available.