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This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas' students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

This book covers the properties and structure of positive linear maps of operator algebras into the bounded operators on Hilbert space.

This volume is devoted to the memory of the applied mathematician Erhard Meister (1930-2001). It is divided into two parts. Part A contains reminiscences about the life of E. Meister including a short biography and an exposition of his professional work. Part B displays the wide range of his scientific interests through eighteen original papers contributed by authors with close scientific and personal relations to Erhard Meister. It covers various fields of mathematical physics and its theoretical background such as partial differential equations, singular integral and pseudodifferential equations as well as topics from operator theory and complex analysis. Altogether fifty colleagues, friends and family members contributed to honour E. Meister as a researcher and promoter of science and succeeded in drawing a real picture of his life and work.§

These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopcedic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer cises is to develop "hand-on" skills in use ofthe techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at tentive, diligent, well-motivated reader.

Since its birth as a mathematical discipline, ergodic theory has had a strong operator theoretic flavor. This graduate text focuses on the interplay between ergodic theory and operator theory in hopes to foster new research that will lead to yet unknown connections between operator theory and ergodic theory in the future. Some recent applications of ergodic theory to combinatorial number theory use sophisticated operator theoretic constructions. On the other hand, results and problems from ergodic theory, once formulated in operator theoretic terms, inspired the development of functional analytic theories with stunning applications. This text develops the operator theory that is significant for or inspired by ergodic theory in a systematic and concise way. The reader is not expected to have any prior encounter with ergodic theory, so it can also serve as an introduction to ergodic theory from a functional analytic perspective. The book can be used for advanced master s and beginning doctoral level classes in the following areas: ergodic theory or dynamical systems with an emphasis on ergodic theorems; functional analysis or operator theory with applications to dynamical system theory; and semigroup methods in dynamical systems. It may also be used as a reference text by researchers in both ergodic and operator theory, and functional analysts who want to make their first steps in ergodic theory. Prerequisites include a familiarity with basic functional analysis, measure theory and topology, but the necessary background is collected in Appendices A-C.