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

2011/10/26 by Han, Deguang, Larson, David R., Liu, Bei +1 · 2 citations
#46B15 #46B25 #46G10 #46L07 #46L10 #46L51 #47A20 (Primary) 42C15 #47B48 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1110.5833

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.

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• Rescaling of unconditional Schauder frames in Hilbert spaces and completely bounded maps
• Approximation properties and quantitative estimation for uniform ball-covering property of operator spaces

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