On the geometry of projections in certain operator algebras

From MaRDI portal
Publication:2653490

DOI10.2307/1969620zbMath0064.11002OpenAlexW2322880091WikidataQ57255510 ScholiaQ57255510MaRDI QIDQ2653490

H. A. Dye

Publication date: 1955

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1969620




Related Items (67)

Surjective isometries between unitary sets of unital JB\(^\ast \)-algebrasContextuality and the fundamental theorems of quantum mechanicsSymmetries of C ∗-algebras and Jordan Morphisms\(L\)-algebras and three main non-classical logicsSelf-similar monoids related to Hahn groupsStructure groups of \(L\)-algebras and Hurwitz actionSpectral order on \(AW^\ast\)-algebras and its preserversOn the extension of unitary group automorphisms of Cuntz algebrasSpectral order of operators and range projectionsOn the extension of unitary group isomorphisms of unital UHF-algebrasThe structure group of a non-degenerate effect algebraCan one identify two unital JB*-algebras by the metric spaces determined by their sets of unitaries?Maps on positive cones of \(C^*\)-algebrasActive lattices determine \(\mathrm{AW}^\ast\)-algebrasRing isomorphisms of type II∞$_\infty$ locally measurable operator algebrasStar order on operator and function algebras and its nonlinear preserversSpectral order isomorphisms and AW$AW$*‐factorsSpectral presheaves as quantum state spacesOrder isomorphisms of operator intervals in von Neumann algebrasSpectral latticesOn regular \({}^*\)-algebras of bounded linear operators: a new approach towards a theory of noncommutative Boolean algebrasOrder isomorphisms on effect algebras of the \(\mathrm{C}^\ast\)-algebras of type \(\mathscr{C}(\mathscr{X})\otimes\mathscr{B}(\mathscr{H})\)The paraunitary group of a von Neumann algebraSurjective \(L^p\)-isometries on Grassmann spacesOrder type Tingley's problem for type \(I\) finite von Neumann algebrasUnitary groups as a complete invariantMaps preserving products of commuting elements in von Neumann algebrasLie Isomorphisms of FactorsOn projective equivalence of invariant subspace latticesUnnamed ItemExtension of projection mappingsDye's theorem and Gleason's theorem for \(AW^\ast\)-algebrasLattice isomorphisms between projection lattices of von Neumann algebrasStar order on JBW algebrasOne-sided orthogonality, orthomodular spaces, quantum sets, and a class of Garside groupsBibliography on quantum logics and related structuresIsometries between projection lattices of von Neumann algebrasAdditive Hermitian idempotent preservers between operator algebrasJordan invariants of von Neumann algebras given by abelian subalgebras and Choquet order on state spacesStar order and partial isometries in \(C^\ast\)-algebrasThe positive contractive part of a noncommutative \(L^{p}\)-space is a complete Jordan invariantQuantum spectral symmetriesOrthogonal measures on state spaces and context structure of quantum theoryDisjointness preservers of \(AW^\ast\)-algebrasPiecewise \(^\ast\)-homomorphisms and Jordan maps on \(C^\ast\)-algebras and factor von Neumann algebrasAutomorphisms of spectral lattices of positive contractions on von Neumann algebrasNoncommutative \(L^p\) structure encodes exactly Jordan structureOn the structure of isometries between noncommutative \(L^p\) spacesUnnamed ItemTransition probabilities of normal states determine the Jordan structure of a quantum systemVon Neumann algebras, \(L\)-algebras, Baer*-monoids, and Garside groupsDye's theorem for tripotents in von Neumann algebras and JBW\(^*\)-triplesTingley's problem through the facial structure of operator algebrasLogarithmic submajorisation and order-preserving linear isometriesGeometry of State SpacesMaps preserving quadratic product between positive cones of JBW-algebrasA general Banach-Stone type theorem and applicationsHilbert and Thompson isometries on cones in JB-algebrasHilbert isometries and maximal deviation preserving maps on JB-algebrasSome properties of graphs of closed operatorsAn application of orthoisomorphisms to non-commutative \(L^ p\)-isometriesNonlinear maps on von Neumann algebras preserving the star orderCoherence and incompatability in W*-algebraic quantum theoryActions of \(*\)-morphisms on certain projections of \(C^*\)-matrix algebrasOrtho-sets and Gelfand spectraPure state transformations induced by linear operatorsA new look at local maps on algebraic structures of matrices and operators




This page was built for publication: On the geometry of projections in certain operator algebras