Memoirs of the American Mathematical Society 2013; 84 pp; softcover Volume: 229 ISBN10: 0821891723 ISBN13: 9780821891728 List Price: US$65 Individual Members: US$39 Institutional Members: US$52 Order Code: MEMO/229/1075
 The authors develop elements of a general dilation theory for operatorvalued measures. Hilbert space operatorvalued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the noncb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operatorvalued measures on sigmaalgebras of sets, and the theory of continuous linear maps between \(C^*\)algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or \(\sigma\) weakly, or w*) continuous. Table of Contents  Introduction
 Preliminaries
 Dilation of operatorvalued measures
 Framings and dilations
 Dilations of maps
 Examples
 Bibliography
