Operator-Valued Measures, Dilations, and the Theory of Frames

TL;DR

This paper develops a general dilation theory for operator-valued measures and linear maps, extending known results from frame theory to broader contexts involving operator algebras.

Contribution

It introduces a dilation framework for operator-valued measures and bounded linear maps, generalizing existing results from frame and framing theory.

Findings

Established dilation results for non-completely bounded maps

Extended frame theory concepts to operator algebra settings

Provided new tools for analyzing operator-valued measures

Abstract

We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known results from the theory of frames and framings.