Combination of Vorinostat and Bortezomib in Relapsed or Refractory T-Cell Non-Hodgkin's Lymphoma

The Study Drugs: Vorinostat is designed to cause chemical changes in different groups of proteins that are attached to DNA (the genetic material of cells), which may slow the growth of cancer cells or cause the cancer cells to die. Bortezomib is designed to block a protein that plays a role in cell function and growth. This may cause cancer cells to die. Study Drug Administration: If you are found to be eligible to take part in this study, on Days 1-14 of each 21-day study cycle, you will take vorinostat. Vorinostat capsules are taken by mouth, 2 times a day (1 time in the morning and 1 time in the evening). The capsules must be taken with food (within 30 minutes after a meal). On Days 1, 4, 8, and 11 of all cycles you will receive bortezomib through a needle in your vein. This will take less than 1 minute. If you begin to experience severe or intolerable side effects, the study drug schedule may be stopped for up to 2 weeks. If the side effects improve, you may be able to begin to receive the study drugs again, with a lower dose of bortezomib. The vorinostat dose will not be changed. If you continue to have severe or intolerable side effects with the lower dose of bortezomib, you will be taken off study. Study Visits: On Day 1 of all cycles, the following tests and procedures will be performed: * You will receive the vorinostat capsules (a 14-day supply for each study cycle) and instructions on how to take the drug. You will be instructed to return any unused vorinostat capsules back to the study staff at the end of each cycle. * Your medical history will be recorded, including any drugs that you are taking. * You will be asked about any side effects you may have. * You will have a physical exam. * You will have a neurological exam. On Day 1, 4, 8, and 11 of all cycles, your vital signs will be measured. On Day 8 of all cycles, blood will be drawn (about 5 teaspoons) for routine tests. On Day 1 of every other cycle (Cycles 3, 5, 7, and so on), the following tests and procedures will be performed: * You will have CT scans and/or Positron emission tomography (PET) scans to check the status of the disease. * Blood (about 5 teaspoons) will be drawn for routine tests and to check the status of the disease. * If the doctor thinks it is necessary, you may have a bone marrow aspirate and/or biopsy. You will have computed tomography (CT) scans and/or PET scans, as needed, every 2 cycles (Cycles 2, 4, 6 and so on), to check the status of the disease. Length of Study: You will receive the study drugs for up to 6 months (8 cycles). After 6 months (8 cycles) of receiving the study drugs, if the disease has not gotten worse or has become better, you may be able to stay on study and continue receiving the study drugs. The study drugs would continue to be given at the same dose and on the same schedule. The study visits, blood collections, and optional biopsies will also continue on the same schedule. If the disease gets worse or you develop severe or intolerable side effects at any time, you will be taken off the study drugs. End-of-Study Visit: If you go off study treatment for any reason, you will have an end-of-study visit within 4 weeks of your last dose of study drug or before starting a new treatment. At this visit, the following tests and procedures will be performed: * You will have a physical exam, including a measurement of your vital signs. * You will have a neurological exam. * You will be asked how well you are able to perform the normal activities of daily living (performance status evaluation). * Blood (about 5 teaspoons) will be drawn for routine tests. * You will have a CT scan and PET scans to check the status of the disease. Follow-Up Visits: After you are off study treatment, you will be contacted by phone call every 2 months to check on how you are doing for up to 5 years. These phone calls will last about 5 minutes. Up to 40 patients will take part in this study. All will be enrolled at M. D. Anderson.