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Lipschitz Algebras and Derivations of von Neumann Algebras
Let M be an abelian von Neumann algebra andEan abelian operator M-bimodule. Then the domain of any ultraweakly closed derivation from M intoEis a Lipschitz algebra. Conversely, every LipschitzExpand
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A characterization of the higher dimensional groups associated with continuous wavelets
A subgroup D of GL (n, ℝ) is said to be admissible if the semidirect product of D and ℝn, considered as a subgroup of the affine group on ℝn, admits wavelets ψ ∈ L2(ℝn) satisfying a generalization ofExpand
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Lipschitz algebras and derivations II: exterior differentiation
Abstract Basic aspects of differential geometry can be extended to various non-classical settings: Lipschitz manifolds, rectifiable sets, sub-Riemannian manifolds, Banach manifolds, Wiener space,Expand
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Consistency of a counterexample to Naimark's problem.
  • C. Akemann, N. Weaver
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences…
  • 6 December 2003
We construct a C*-algebra that has only one irreducible representation up to unitary equivalence but is not isomorphic to the algebra of compact operators on any Hilbert space. This answers an oldExpand
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A von Neumann algebra approach to quantum metrics
We propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Our definition effectively reduces to the classical notion in the atomic abelianExpand
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Quantum relations
We define a “quantum relation” on a von Neumann algebra M ⊆ B(H) to be a weak* closed operator bimodule over its commutant M. Although this definition is framed in terms of a particularExpand
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The Calkin algebra has outer automorphisms
Assuming the continuum hypothesis, we show that the Calkin algebra has 2^{aleph_1} outer automorphisms.
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A Lyapunov‐type theorem from Kadison–Singer
Marcus, Spielman, and Srivastava recently solved the Kadison-Singer problem by showing that if u_1, ..., u_m are column vectors in C^d such that \sum u_iu_i^* = I, then a set of indices S \subseteqExpand
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QUANTUM GRAPHS AS QUANTUM RELATIONS
The "noncommutative graphs" which arise in quantum error correction are a special case of the quantum relations introduced in [N. Weaver, Quantum relations, Mem. Amer. Math. Soc. 215 (2012), v-vi,Expand
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Modules with norms which take values in a C*-algebra
We consider modules E over a C*-algebra A which are equipped with a map into A+ that has the formal properties of a norm. We completely determine the structure of these modules. In particular, weExpand
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