Consistency of a counterexample to Naimark's problem.
- C. Akemann, N. Weaver
- MathematicsProceedings of the National Academy of Sciences…
- 6 December 2003
It is proved that the statement "there exists a counterexample to Naimark's problem which is generated by aleph (1) elements" is undecidable in standard set theory.
Quantum relations
- N. Weaver
- Mathematics
- 3 May 2010
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 particular…
Lipschitz algebras and derivations II: exterior differentiation
- N. Weaver
- Mathematics
- 17 July 1998
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,…
The Calkin algebra has outer automorphisms
- N. Phillips, N. Weaver
- Mathematics
- 23 June 2006
Assuming the continuum hypothesis, we show that the Calkin algebra has 2^{aleph_1} outer automorphisms.
Lipschitz Algebras and Derivations of von Neumann Algebras
- N. Weaver
- Mathematics
- 1 August 1996
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 Lipschitz…
A von Neumann algebra approach to quantum metrics
- G. Kuperberg, N. Weaver
- Mathematics
- 3 May 2010
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 abelian…
Quasi-varieties of metric algebras
- N. Weaver
- Mathematics
- 1 March 1995
SET THEORY AND OPERATOR ALGEBRAS
- I. Farah, Eric Wofsey, S. Ghasemi
- Mathematics
- 2010
These notes are based on the six-hour Appalachian Set Theory workshop given by Ilijas Farah on February 9th, 2008 at Carnegie Mellon University. The first half of the workshop (Sections 1–4)…
ℬ(H) has a pure state that is not multiplicative on any masa
- C. Akemann, N. Weaver
- MathematicsProceedings of the National Academy of Sciences
- 8 April 2008
It is proved that ℬ(H) has a pure state whose restriction to any masa is not pure and this resolves negatively old conjectures of Kadison and Singer and of Anderson.
Quantum Graphs as Quantum Relations
- N. Weaver
- MathematicsJournal of Geometric Analysis
- 12 June 2015
The “noncommutative graphs” which arise in quantum error correction are a special case of the quantum relations introduced in Weaver (Quantum relations. Mem Am Math Soc 215(v–vi):81–140, 2012). We…
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