Inclusion Criteria:

          -  Relapsed and refractory PTCL, including angioimmunoblastic T-cell lymphoma (AITL),
             anaplastic large cell lymphoma (ALCL) ALK+/ALK-, adult T-cell leukemia/lymphoma
             (ATLL), NK-cell lymphoma (NKL), transformed MF to large cell, and PTCL-unspecified
             (PTCL-U) patients who have failed standard therapy/transplant for their histological
             confirmed disease or who are not transplant eligible are eligible to participate in
             this trial

          -  Karnofsky performance status >= 70

          -  ANC >= 700 cells/mm^3, unless due to lymphoma involvement of the bone marrow or spleen

          -  Platelet count >= 50 mm^3, unless due to lymphoma involvement of the bone marrow or
             spleen

          -  Hemoglobin >= 8 g/dL, unless due to lymphoma involvement of the bone marrow

          -  Liver functions (AST, ALT, bilirubin) =< 3 x upper limits of normal (ULN) unless due
             to lymphoma or due to Gilberts disease

          -  Serum creatinine < 2.0 mg/dL or calculated creatinine clearance (CrCl) > 40 mL/min
             (Cockcroft-Gault)

          -  LVEF >= 40% 2-D transthoracic ECHO is the preferred method of evaluation; MUGA scan is
             acceptable if ECHO is not available

          -  Able to adhere to the study visit schedule and other protocol requirements

          -  Patients must be willing to give written informed consent, and sign an institutionally
             approved consent form before performance of any study-related procedure not part of
             normal medical care, with the understanding that consent may be withdrawn by the
             subject at any time without prejudice to future medical care

          -  Non-pregnant and non-nursing; men and women of reproductive potential may not
             participate unless they have agreed to use an effective contraceptive method while on
             the study

          -  No serious disease or condition that, in the opinion of the investigator, would
             compromise the patient's ability to participate in the study

          -  Patients with a history of coronary artery disease, congestive heart failure,
             hypertension, diabetes, or hyperlipidemia must have a MUGA or echocardiography,
             performed within 2 months of study entry

        Exclusion Criteria:

          -  Pregnant or breast feeding females

          -  Active serious infection requiring treatment within 14 days prior to the start of
             carfilzomib

          -  Active hepatitis or uncontrolled HIV

          -  Unstable angina or myocardial infarction within 6 months prior to enrollment, New York
             Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, history
             of severe coronary artery disease, severe uncontrolled ventricular arrhythmias, sick
             sinus syndrome, or EKG evidence of acute ischemia or Grade 3 conduction system
             abnormalities unless subject has a pacemaker

          -  Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to the start
             of carfilzomib

          -  Patients in whom the schedule of oral and IV fluid hydration is contraindicated, e.g.,
             due to pre-existing pulmonary, cardiac, or renal impairment

          -  Prior malignancies within the past 2 years with exception of adequately treated basal
             cell, squamous cell skin cancer, or thyroid cancer; carcinoma in situ of the cervix or
             breast; prostate cancer of Gleason grade 6 or less with stable prostate specific
             antigen (PSA) levels

          -  Significant peripheral neuropathy (grades 3-4, or grade 2 with pain) within 14 days
             prior to the start of carfilzomib

          -  Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize
             carfilzomib)

          -  Concurrent use of other anti-cancer agents, investigative agents, or treatments

          -  Contraindication to any of the required concomitant drugs or supportive treatments,
             including hypersensitivity to all anticoagulation and antiplatelet options, antiviral
             drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment

          -  Any other clinically significant medical disease or condition laboratory abnormality
             or psychiatric illness that, in the Investigator's opinion, may interfere with
             protocol adherence or a subject's ability to give informed consent