Memoirs of the American Mathematical Society 1993; 109 pp; softcover Volume: 101 ISBN10: 0821825453 ISBN13: 9780821825457 List Price: US$29 Individual Members: US$17.40 Institutional Members: US$23.20 Order Code: MEMO/101/484
 Through classification of compact abelian group actions on semifinite injective factors, Jones and Takesaki introduced the notion of an action of a measured groupoid on a von Neumann algebra, which has proven to be an important tool for this kind of analysis. Elaborating on this notion, this work introduces a new concept of a measured groupoid action that may fit more perfectly into the groupoid setting. Yamanouchi also shows the existence of a canonical coproduct on every groupoid von Neumann algebra, which leads to a concept of a coaction of a measured groupoid. Yamanouchi then proves duality between these objects, extending NakagamiTakesaki duality for (co)actions of locally compact groups on von Neumann algebras. Readership Research mathematicians. Table of Contents  Relative tensor products of Hilbert spaces over abelian von Neumann algebras
 Coproducts of groupoid von Neumann algebras
 Actions and coactions of measured groupoids on von Neumann algebras
 Crossed products by groupoid actions and their dual coactions
 Crossed products by groupoid coactions and their dual actions
 Duality for actions on von Neumann algebras
 Duality for integrable coactions on von Neumann algebras
 Examples of actions and coactions of measured groupoids on von Neumann algebras
