Adoptive Cord Blood Immunotherapy for EBV, CMV, BKV and Adenovirus Reactivation/Infection or Prophylaxis

Each cohort of 2 patients will be treated and observed for 45 days for toxicity, dose escalation, and GvHD. The algorithm of sequentially adaptive EffTox trade-off-based design of Thall et al will be used to determine the dose for each cohort. If 1x107CTL/m2 results in unacceptable toxicity or efficacy, the study will be closed to accrual.