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Theory of Operator Algebras II
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The article was published on 1979-01-01 and is currently open access. It has received 3776 citations till now. The article focuses on the topics: Nest algebra & Ladder operator.read more
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Divided Differences in Noncommutative Geometry: Rearrangement Lemma, Functional Calculus and Expansional Formula
TL;DR: In this article, a generalization of the Connes-Tretkoff-Moscovici Rearrangement Lemma is presented, which is based on the calculus of divided differences.
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Hochschild cohomology of factors with property $\Gamma$
TL;DR: The main result of as mentioned in this paper is that the k th continuous Hochschild cohomology groups of a von Neumann factor M⊆ B(H )o f with property Γ are zero for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps.
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Localized endomorphisms in Kitaev's toric code on the plane
TL;DR: In this article, the authors considered various aspects of Kitaev's toric code model on a plane in the C^*-algebraic approach to quantum spin systems on a lattice and showed that elementary excitations of ground state can be described by localized endomorphisms of the observable algebra.
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Projections, multipliers and decomposable maps on noncommutative $\mathrm{L}^p$-spaces
TL;DR: In this article, a non-commutative analogue of the absolute value of a regular operator acting on a noncommutive space is described. But the analogue does not cover all classes of regular multipliers, including Schur and Fourier multipliers.
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The Dixmier property and tracial states for C⁎-algebras
TL;DR: In this paper, the N.A.T. was partially supported by an NSERC Postdoctoral Fellowship and through the EPSRC grant EP/N00874X/1.