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Operator-Valued Measures, Dilations, and the Theory of Frames
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Operator-Valued Measures, Dilations, and the Theory of Frames
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eBook
Operator-Valued Measures, Dilations, and the Theory of Frames
2013
Overview
We 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 our 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. We 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
Publisher
American Mathematical Society
ISBN
0821891723, 9780821891728
