Operator-valued measures, dilations, and the theory of frames
Author(s)
Bibliographic Information
Operator-valued measures, dilations, and the theory of frames
（Memoirs of the American Mathematical Society, no. 1075）
American Mathematical Society, c2013
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Other authors: David R. Larson, Bei Liu, Rui Liu
"Volume 229, number 1075 (second of 5 numbers), May 2014"
Includes bibliographical references (p. 83-84)
Description and Table of Contents
Description
The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued 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 non-cb 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 operator-valued measures on sigma-algebras 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 σ weakly, or w*) continuous.
Table of Contents
Introduction
Preliminaries Dilation of operator-valued measures
Framings and dilations
Dilations of maps
Examples
Bibliography
by "Nielsen BookData"
