All automorphisms of the Calkin algebra are inner

DOI10.4007/annals.2011.173.2.1zbMath1250.03094arXiv0705.3085OpenAlexW2118212674WikidataQ56031481 ScholiaQ56031481MaRDI QIDQ640751

Ilijas Farah

Publication date: 20 October 2011

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

Full work available at URL: https://arxiv.org/abs/0705.3085

zbMATH Keywords

continuum hypothesisindependence resultsouter automorphismsCalkin algebraapproximate homomorphismsTodorcevic's axiom

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Consistency and independence results (03E35) Continuum hypothesis and Martin's axiom (03E50) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (39)

Trivial endomorphisms of the Calkin algebra ⋮ Rigidity conjectures for continuous quotients ⋮ Essentially spectrally bounded linear maps ⋮ RIGIDITY OF CONTINUOUS QUOTIENTS ⋮ On automorphisms of the Banach space $\ell _\infty /c_0$ ⋮ Some Calkin algebras have outer automorphisms ⋮ Some remarks on the open coloring axiom ⋮ Isomorphisms of quotients of FDD-algebras ⋮ Separable spaces of continuous functions as Calkin algebras ⋮ What makes the continuum ℵ₂ ⋮ Stability of a general functional equation in \(m\)-Banach spaces ⋮ Determinacy axioms and large cardinals ⋮ The Calkin algebra, Kazhdan's property (T), and strongly self‐absorbing C∗$\mathrm{C}^*$‐algebras ⋮ On the commutant of \(B(H)\) in its ultrapower ⋮ Homeomorphisms of Čech–Stone remainders: the zero-dimensional case ⋮ On perturbations of two general equations in several variables ⋮ REDUCED PRODUCTS OF METRIC STRUCTURES: A METRIC FEFERMAN–VAUGHT THEOREM ⋮ On Ulam stability of a functional equation ⋮ On the consistency strength of the proper forcing axiom ⋮ Model theory of operator algebras. II: Model theory ⋮ Trivial automorphisms ⋮ Gaps in the poset of projections in the Calkin algebra ⋮ On linear maps preserving generalized invertibility and related properties ⋮ A hierarchy of tree-automatic structures ⋮ AN INVITATION TO MODEL THEORY AND C*-ALGEBRAS ⋮ On maximal ideals which are also minimal prime ideals in certain Banach rings ⋮ Saturation and elementary equivalence of \(C^\ast\)-algebras ⋮ Forcing axioms and coronas of C∗-algebras ⋮ Automorphisms of corona algebras, and group cohomology ⋮ Ultrametric Calkin algebras ⋮ Martin's maximum\(^{++}\) implies Woodin's axiom \((*)\) ⋮ Martin's maximum revisited ⋮ Category forcings, 𝑀𝑀⁺⁺⁺, and generic absoluteness for the theory of strong forcing axioms ⋮ On the generalized Hyers-Ulam stability of a functional equation and its consequences ⋮ Uniform Roe coronas ⋮ Can we resolve the continuum hypothesis? ⋮ On the pointwise implementation of near-actions ⋮ The Calkin algebra is not countably homogeneous ⋮ \(C^{*}\)-algebras with and without \(\ll\)-increasing approximate units

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