RATIONALE: Donor peripheral stem cell transplantation may be able to replace bone marrow and immune cells that were destroyed by chemotherapy. Sometimes the transplanted cells from a donor are rejected by the body's normal cells. Eliminating the T cells from the donor cells before transplanting them and giving cyclosporine may prevent this from happening. PURPOSE: This phase I trial is studying the side effects of T-cell-depleted allogeneic stem cell transplantation after immunoablative induction chemotherapy and reduced-intensity transplantation conditioning (chemotherapy) in treating patients with hematologic malignancies.
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