Operator-Valued Measures, Dilations, and the Theory of Frames
Apr 2014 · American Mathematical Soc.
Ebook
84
Pages
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About this ebook
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;)
-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 weakly, or w*) continuous.
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
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
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