This volume consists of articles contributed by participants at the fourth Ja- pan-U.S. Joint Seminar on Operator Algebras. The seminar took place at the University of Pennsylvania from May 23 through May 27, 1988 under the auspices of the Mathematics Department. It was sponsored and supported by the Japan Society for the Promotion of Science and the National Science Foundation (USA). This sponsorship and support is acknowledged with gratitude. The seminar was devoted to discussions and lectures on results and prob- lems concerning mappings of operator algebras (C*-and von Neumann alge-...