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

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.

88 pages, to appear in Memoirs of the American Mathematical Society

References in corpus (1)

• Coefficient Quantization for Frames in Banach Spaces

Cited by in corpus (10)

• Dilations for Systems of Imprimitivity acting on Banach Spaces
• $C^{\ast }$-extreme points of positive operator valued measures and unital completely positive maps
• On Operator Valued Measures
• There are no unconditional Schauder frames of translates in $L^p(\mathbb{R})$, $1\le p\le 2$
• L${}^p$ spaces of operator-valued functions
• Extension of frames and bases -- II
• Bistochastic operators and quantum random variables
• Dilations for operator-valued quantum measures
• Hilbert-Schauder Frame Operators
• Operator-Valued Frames for the Heisenberg Group