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

DOI10.1090/memo/1075zbMath1323.46031arXiv1110.5833OpenAlexW4245769974MaRDI QIDQ2925675

David R. Larson, Bei Liu, Rui Liu, De Guang Han

Publication date: 17 October 2014

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5833

zbMATH Keywords

framesvon Neumann algebrasdilationscompletely bounded mapsnormal mapsoperator-valued measures

Mathematics Subject Classification ID

Classical Banach spaces in the general theory (46B25) General theory of von Neumann algebras (46L10) Operator spaces and completely bounded maps (46L07) Noncommutative measure and integration (46L51) Dilations, extensions, compressions of linear operators (47A20) Linear operators on Banach algebras (47B48) General harmonic expansions, frames (42C15) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Vector-valued measures and integration (46G10)

Related Items (25)

Generalized Choi-Kraus dilations of linear maps between matrix algebras ⋮ Continuous framings for Banach spaces ⋮ On Operator Valued Measures ⋮ On some dual frames multipliers with at most countable spectra ⋮ Quantum injectivity of multi-window Gabor frames in finite dimensions ⋮ Structural properties of homomorphism dilation systems ⋮ Dilations of dual \(g\)-frame generators for an abstract wavelet system ⋮ On the continuous frame quantum detection problem ⋮ Dilations for operator-valued quantum measures ⋮ Operator-valued frames for the Heisenberg group ⋮ Dilations of operator-valued measures with bounded \(p\)-variations and framings on Banach spaces ⋮ Unnamed Item ⋮ Partial isometries and a general spectral theorem ⋮ Injective continuous frames and quantum detections ⋮ Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions ⋮ Parseval \(p\)-frames and the Feichtinger conjecture ⋮ Positive operator-valued measures and densely defined operator-valued frames ⋮ Frame vector multipliers for finite group representations ⋮ \(\mathrm{L}^p\) spaces of operator-valued functions ⋮ Mixed-state localization operators: Cohen's class and trace class operators ⋮ Characterization of alternate duals of continuous frames and representation frames ⋮ Dilations for systems of imprimitivity acting on Banach spaces ⋮ An operator-valued Lyapunov theorem ⋮ \(C^*\)-extreme points of positive operator valued measures and unital completely positive maps ⋮ Frames and finite-rank integral representations of positive operator-valued measures

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