Ergodic decomposition of a stationary channel operator |
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| Institution: | 1. Department of Medicine, Division of Allergy, Pulmonary and Critical Care Medicine, Vanderbilt University School of Medicine, Nashville, TN, USA;2. Department of Psychiatry, Vanderbilt University School of Medicine, Nashville, TN, USA;3. Center for Health Services Research, Vanderbilt University School of Medicine, Nashville, TN, USA;4. Department of Anesthesiology, Division of Critical Care, Vanderbilt University School of Medicine, Nashville, TN, USA;5. Department of Biostatistics, Vanderbilt University School of Medicine, Nashville, TN, USA;6. Department of Medicine, Division of General Internal Medicine and Public Health, Vanderbilt University School of Medicine, Nashville, TN, USA;7. Research Service, Department of Veterans Affairs Medical Center, Tennessee Valley Healthcare System, Nashville, TN, USA;8. Anesthesia Service, Department of Veterans Affairs Medical Center, Tennessee Valley Healthcare System, Nashville, TN, USA;9. Geriatric Research, Education and Clinical Center (GRECC) Service, Department of Veterans Affairs Medical Center, Tennessee Valley Healthcare System, Nashville, TN, USA;10. Rehabilitation and Aged Care Unit Hospital Ancelle, Cremona, Italy;11. Geriatric Research Group, Brescia, Italy;12. Department of Medicine, Pulmonary and Critical Care Division, Intermountain Medical Center, Murray, UT, USA;13. Psychology Department and Neuroscience Center, Brigham Young University, Provo, UT, USA;1. Department of Statistics, Faculty of Commerce, Zagazig University, Egypt;2. Department of Statistics, Mathematics and Insurance, Benha University, Egypt;3. Department of Statistics, St. Anthony’s College, Shillong-793001, Meghalaya, India;4. Department of Statistics, Central University of Haryana, Mahendergarh, India |
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| Abstract: | Pointwise weak* topology is defined for the set of all channel operators and the latter is shown to be compact with this topology. Since the set of all ergodic stationary channel operators coincides with the set of all extreme points of the set of stationary channel operators, each stationary channel operator is represented as an integral of ergodic stationary channel operators with respect to a suitable probability measure on the set of all ergodic stationary channel operators. |
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