Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
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Publication:2572176
DOI10.1007/3-540-28517-2zbMath1092.46003OpenAlexW4252290972MaRDI QIDQ2572176
Publication date: 16 November 2005
Published in: Encyclopaedia of Mathematical Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/3-540-28517-2
General theory of von Neumann algebras (46L10) General theory of (C^*)-algebras (46L05) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02)
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II ⋮ Quantization of Hamiltonian loop group spaces ⋮ Strong Morita equivalence for completely positive linear maps on \(C^\ast\)-algebras ⋮ Characterization of numerical radius parallelism in \(C^*\)-algebras ⋮ Triangular \(C^{\ast}\)-bialgebra defined as the direct sum of matrix algebras ⋮ Commutators in \(C^\ast\)-algebras and traces ⋮ Groupoid algebras as Cuntz-Pimsner algebras ⋮ Lifting Bratteli diagrams between Krajewski diagrams: spectral triples, spectral actions, and \textit{AF} algebras ⋮ On stably finiteness for \(C^*\)-algebras of exponential solvable Lie groups ⋮ Omitting types and AF algebras ⋮ Fixed point composition and Toeplitz-composition \(C^\ast\)-algebras ⋮ Nuclearity of semigroup \(C^\ast\)-algebras and the connection to amenability ⋮ Metrics and causality on Moyal planes ⋮ Numerical radius and product of elements in C*-algebras ⋮ Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras ⋮ Fixed points of compact quantum groups actions on Cuntz algebras ⋮ Generalised morphisms of 𝑘-graphs: 𝑘-morphs ⋮ Enlargeability and index theory: infinite covers ⋮ Extensions of operator algebras. I. ⋮ Characterization of tracial functionals on von Neumann algebras ⋮ Unitary equivalence of automorphisms of separable \(C^*\)-algebras ⋮ The resolvent algebra: ideals and dimension ⋮ Crossed products of \(C^\ast\)-algebras for singular actions ⋮ Measures and Dirichlet forms under the Gelfand transform ⋮ Semiprojectivity with and without a group action ⋮ Determining elements in \(C^\ast\)-algebras through spectral properties ⋮ The local multiplier algebra of a \(C^\ast\)-algebra with finite dimensional irreducible representations ⋮ A new look at crossed product correspondences and associated \(C^\ast\)-algebras ⋮ Brown measure support and the free multiplicative Brownian motion ⋮ The $K$-theory of Toeplitz $C^*$-algebras of right-angled Artin groups ⋮ A quantitative version of Herstein’s theorem for Jordan ∗-isomorphisms ⋮ The \(C^*\)-algebra of the Heisenberg motion groups \(\mathbb{T}^n\times\mathbb{H}_n\) ⋮ Manifolds of classical probability distributions and quantum density operators in infinite dimensions ⋮ A non-commutative model for higher twistedK-theory ⋮ Purely infinite partial crossed products ⋮ Ultraproducts of von Neumann algebras ⋮ Riesz bases associated with regular representations of semidirect product groups ⋮ Projections and traces on von Neumann algebras ⋮ Cycline subalgebras of 𝑘-graph C*-algebras ⋮ A new proof of the Tikuisis-White-Winter theorem ⋮ Involutive operator algebras ⋮ Operator-valued chordal Loewner chains and non-commutative probability ⋮ A \(C^*\)-algebra construction for undirected graphs ⋮ Transition probability preserving maps on a Grassmann space in a semifinite factor ⋮ Chain conditions for graph C*-algebras ⋮ A DICHOTOMY FOR THE NUMBER OF ULTRAPOWERS ⋮ Chain conditions for \(C^\ast\)-algebras coming from Hilbert \(C^\ast\)-modules ⋮ \(C^{*}\)-algebras with and without \(\ll\)-increasing approximate units ⋮ Branching systems and general Cuntz–Krieger uniqueness theorem for ultragraph C*-algebras ⋮ Rokhlin actions on inner quasidiagonal $C^\ast $-algebras ⋮ Continuity of functors with respect to generalized inductive limits ⋮ Residually finite-dimensional operator algebras ⋮ Embedding semigroup \(C^\ast\)-algebras into inductive limits ⋮ Locally trivial W∗-bundles ⋮ Model theory and Rokhlin dimension for compact quantum group actions ⋮ $C^{*}$-algebras associated with real multiplication ⋮ Noncommutative semialgebraic sets and associated lifting problems ⋮ Lower bounds on matrix factorization ranks via noncommutative polynomial optimization ⋮ Derivations of subhomogeneous $C^*$-algebras are implemented by local multipliers ⋮ Finite decomposition rank for virtually nilpotent groups ⋮ NORMAL SUBGROUPS, CENTER AND INNER AUTOMORPHISMS OF COMPACT QUANTUM GROUPS ⋮ On Kirchberg's embedding problem ⋮ Real dimensional spaces in noncommutative geometry ⋮ Stability of the Wigner equation -- a singular case ⋮ \(^\ast\)-Annihilators in proper \(^\ast\)-semigroups ⋮ Weak\(^*\)-2-local derivations on semi-finite von Neumann algebras ⋮ The nuclear dimension of \(\mathcal{O}_\infty \)-stable \(C^\ast \)-algebras ⋮ Commutativity of central sequence algebras ⋮ Strongly outer actions of amenable groups on \(\mathcal{Z}\)-stable nuclear \(C^\ast\)-algebras ⋮ Multiplier tests and subhomogeneity of multiplier algebras ⋮ Semifinite harmonic functions on branching graphs ⋮ Absolute compatibility and Poincaré sphere ⋮ A uniqueness theorem for twisted groupoid \(C^{*}\)-algebras ⋮ Smooth lattice orbits of nilpotent groups and strict comparison of projections ⋮ The ideal structure of \(C^\ast\)-algebras related to lattice-ordered groups ⋮ Local version of approximation theorem and of \(\lambda\)-tensor product of operator systems ⋮ General uniform Roe algebra rigidity ⋮ Tolerance relations and quantization ⋮ Cutoff profiles for quantum Lévy processes and quantum random transpositions ⋮ Band projections and decomposition of normal traces on von Neumann algebras ⋮ Krull dimension for \(\mathrm{C}^{\star}\)-algebras ⋮ Analytic lifts of operator concave functions ⋮ The primitive spectrum of a semigroup of Markov operators ⋮ Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics ⋮ Discrete convolution operators and Riesz systems generated by actions of abelian groups ⋮ Property \(T\) and strong property \(T\) for unital \(*\)-homomorphisms ⋮ Pro-\(C^*\)-algebras associated with pro-\(C^*\)-correspondences versus tensor products ⋮ Inductive limits of projective \(C^\ast\)-algebras ⋮ Elliptic operators and \(K\)-homology ⋮ Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups ⋮ Metrics on projections of the von Neumann algebra associated with tracial functionals ⋮ Cartan subalgebras for non-principal twisted groupoid \(C^\ast\)-algebras ⋮ Linear combination of projections in von Neumann factors ⋮ Absolutely compatible pair of elements in a von Neumann algebra. II ⋮ Loewner's theorem in several variables ⋮ The Calkin algebra is \(\aleph_1\)-universal ⋮ On the notion of noncommutative submanifold ⋮ Orthograph related to mutual strong Birkhoff-James orthogonality in \(C^*\)-algebras ⋮ QCD on an infinite lattice ⋮ Universal decomposition equalities for operator matrices in a Hilbert space ⋮ Subalgebras of simple AF-algebras ⋮ Orthogonally additive polynomials on non-commutative \(L^p\)-spaces ⋮ Classical dynamics generated by long-range interactions for lattice fermions and quantum spins ⋮ A non-nuclear \(C^*\)-algebra with the weak expectation property and the local lifting property ⋮ A generalization of Voiculescu's theorem for normal operators to semifinite von Neumann algebras ⋮ Nuclearity of semigroup \(C^\ast \)-algebras ⋮ The generator rank of \(C^\ast \)-algebras ⋮ Partial isometries in an absolute order unit space ⋮ Approximate ideal structures and \(K\)-theory ⋮ The weak tracial Rokhlin property for finite group actions on simple $C^*$-algebras ⋮ Complete order equivalence of spin unitaries ⋮ Scaling limits of lattice quantum fields by wavelets ⋮ Characterizing traces on crossed products of noncommutative \(\mathrm{C}^\ast\)-algebras ⋮ Gateaux derivative of \(C^\ast\) norm ⋮ Birkhoff-James orthogonality and applications: a survey ⋮ Equivariant property (SI) revisited ⋮ On vector-valued characters for noncommutative function algebras ⋮ Inductive limits of compact quantum groups and their unitary representations ⋮ Representations of nets of \(C^{*}\)-algebras over \(S ^{1}\) ⋮ Mapping ideals of quantum group multipliers ⋮ \(L^p-L^q\) multipliers on locally compact groups ⋮ Deciphering the algebraic CPT theorem ⋮ \(C^{\ast}\)-algebras associated to graphs of groups ⋮ Hopf images in locally compact quantum groups ⋮ Twisted \(k\)-graph algebras associated to Bratteli diagrams ⋮ Compact hypergroups from discrete subfactors ⋮ Approximately order zero maps between \(\mathrm{C}^\ast \)-algebras ⋮ Nuclear dimension of crossed products associated to partial dynamical systems ⋮ Spectral truncations in noncommutative geometry and operator systems ⋮ \(K_0\)-group of absolute matrix order unit spaces ⋮ Operators preserving mutual strong Birkhoff-James orthogonality on \(\mathcal{B}(H)\) ⋮ Exactness versus \(C^*\)-exactness for certain non-discrete groups ⋮ Partial actions of \(C^{*}\)-quantum groups ⋮ Projections on von Neumann algebras as limits of elementary operators ⋮ Tensor products of hyperrigid operator systems ⋮ On inductive limits for systems of \(C^\ast\)-algebras ⋮ Secondary cup and cap products in coarse geometry ⋮ The nuclear dimension of \(C^\ast \)-algebras associated to topological flows and orientable line foliations ⋮ Operator space tensor products and inductive limits ⋮ Completely order bounded maps on non-commutative \(L_p\)-spaces ⋮ \(\mathcal{C}u\)-nuclearity implies LLP and exactness ⋮ Quantum graphs as quantum relations ⋮ Generalized Rickart \(\ast \)-rings ⋮ Trace inequalities for Rickart \(C^{\ast}\)-algebras ⋮ Essential numerical ranges of operators in semi-Hilbertian spaces ⋮ Covering dimension of Cuntz semigroups ⋮ Dilation theory in finite dimensions and matrix convexity ⋮ Injective tensor products in strict deformation quantization ⋮ Von Neumann algebra conditional expectations with applications to generalized representing measures for noncommutative function algebras ⋮ Lifting spectral triples to noncommutative principal bundles ⋮ Reversible part of quantum dynamical systems: a review ⋮ Monadic forgetful functors and (non-)presentability for \(C^\ast\)- and \(W^\ast\)-algebras ⋮ AF-algebras with lattice-ordered \(K_0\): logic and computation ⋮ A converse to Lieb-Robinson bounds in one dimension using index theory ⋮ Finite approximation properties of \(C^\ast\)-modules ⋮ Haar systems, KMS states on von Neumann algebras and \(C^*\)-algebras on dynamically defined groupoids and noncommutative integration ⋮ Invertibility of the operators on Hilbert spaces and ideals in \(C^*\)-algebras ⋮ A note on commutation relations and finite dimensional approximations ⋮ \(C^\ast\) completions of Leavitt-path-algebra pullbacks ⋮ Characterization of certain traces on von Neumann algebras ⋮ Von Neumann equivalence and group exactness ⋮ Amenability and approximation properties for partial actions and Fell bundles ⋮ Slant products on the Higson-Roe exact sequence ⋮ Ideal submodules versus ternary ideals versus linking ideals ⋮ Differences and commutators of projections on a Hilbert space
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