Extensions, Restrictions, and Representations of States on C ∗ - Algebras
From MaRDI portal
Publication:4195439
DOI10.2307/1998793zbMath0408.46049OpenAlexW4247782205WikidataQ60174474 ScholiaQ60174474MaRDI QIDQ4195439
Publication date: 1979
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/1998793
RestrictionsExtensionsRepresentationsC*-AlgebrasUltrafilterMaximal Abelian SubalgebraPure StateStone Cech Compactification
General theory of von Neumann algebras (46L10) Commutators, derivations, elementary operators, etc. (47B47) General theory of (C^*)-algebras (46L05) Dilations, extensions, compressions of linear operators (47A20) States of selfadjoint operator algebras (46L30) Dual spaces of operator algebras (47L50)
Related Items
Quantum measurable cardinals ⋮ Restricted invertibility of continuous matrix functions ⋮ The relative Dixmier property in discrete crossed products ⋮ Sampling discretization and related problems ⋮ Paving property for real stable polynomials and strongly Rayleigh processes ⋮ Cartan subalgebras in \(C^\ast\)-algebras of Hausdorff étale groupoids ⋮ Compact operators in type \(III_{\lambda}\) and type \(III_ 0\) factors. I ⋮ A uniqueness theorem for twisted groupoid \(C^{*}\)-algebras ⋮ The Kadison-Singer problem ⋮ Topologically free actions and ideals in discrete C*-dynamical systems ⋮ A non-diagonalizable pure state ⋮ Mixed determinants and the Kadison-Singer problem ⋮ Extreme points in sets of positive linear maps on \(\mathcal B (\mathcal H)\) ⋮ Properties and applications of a conjugate transform on Schatten classes ⋮ Improved bounds in Weaver's \(\operatorname{KS}_r\) conjecture for high rank positive semidefinite matrices ⋮ A decomposition theorem for frames and the Feichtinger Conjecture ⋮ A Dixmier-Douady theorem for Fell algebras ⋮ Paving small matrices and the Kadison-Singer extension problem. II: Computational results ⋮ The Kadison-Singer problem for the direct sum of matrix algebras ⋮ Paved with good intentions: analysis of a randomized block Kaczmarz method ⋮ A II\(_{1}\) factor approach to the Kadison-Singer problem ⋮ The discretization problem for continuous frames ⋮ Some new equivalences of Anderson’s paving conjectures ⋮ A dynamical systems approach to the Kadison-Singer problem ⋮ Calkin images of Fourier convolution operators with slowly oscillating symbols ⋮ Improved bounds in Weaver and Feichtinger conjectures ⋮ The relative dixmier property for inclusions of von Neuman algebras of finite index ⋮ Simplicity of algebras associated to non-Hausdorff groupoids ⋮ Singular states on maximal \(Op^ *\)-algebras ⋮ CARTAN SUBALGEBRAS IN DIMENSION DROP ALGEBRAS ⋮ Extensions of pure states and projections of norm one ⋮ The legacy of Jean Bourgain in geometric functional analysis ⋮ Pseudo-diagonals and uniqueness theorems ⋮ Interlacing families. II: Mixed characteristic polynomials and the Kadison-Singer problem ⋮ The Kadison-Singer problem ⋮ Splitting for subalgebras of tensor products