Positive sesquilinear form measures and generalized eigenvalue expansions

DOI10.1016/j.jmaa.2007.03.051zbMath1127.47023arXivmath/0703589OpenAlexW2057077260MaRDI QIDQ2381937

Juha-Pekka Pellonpää, Kari Ylinen, Tuomas P. Hytönen

Publication date: 26 September 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703589

zbMATH Keywords

normal operatorgeneralized eigenvectordirect integralsesquilinear formNaimark dilation(semi)spectral measure

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Eigenvalue problems for linear operators (47A75)

Related Items (11)

Naimark dilations of qubit POVMs and joint measurements ⋮ Optimal quantum observables ⋮ Covariant KSGNS construction and quantum instruments ⋮ Modules, completely positive maps, and a generalized KSGNS construction ⋮ Modular sesquilinear forms and generalized Stinespring representation ⋮ Diagonalization and representation results for nonpositive sesquilinear form measures ⋮ Complete measurements of quantum observables ⋮ Operator integrals and sesquilinear forms ⋮ Modules and extremal completely positive maps ⋮ Frames and finite-rank integral representations of positive operator-valued measures ⋮ Extreme covariant quantum observables in the case of an Abelian symmetry group and a transitive value space

Cites Work

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• A fundamental approach to the generalized eigenvalue problem for self- adjoint operators
• Normal covariant quantization maps
• Maximality of positive operator-valued measures
• Characterizations of the canonical phase observable
• Phase observables, phase operators and operator orderings
• Covariant localizations in the torus and the phase observables
• Operational Quantum Physics
• Stochastic Equations in Infinite Dimensions

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