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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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Proceedings ArticleDOI
The noncommutative geometry of aperiodic solids
TL;DR: In this paper, the gap labeling theorem and the Anderson-Putnam complex of aperiodic, repetitive, FLC tiling spaces are discussed, and the concept of Hull is introduced.
Journal ArticleDOI
Type III factors with unique Cartan decomposition
Cyril Houdayer,Stefaan Vaes +1 more
TL;DR: In this article, it was shown that for any free ergodic nonsingular nonamenable action Γ ↷ ( X, μ ) of all Γ in a large class of groups including all hyperbolic groups, the associated group measure space von Neumann algebra has L ∞ ( X ) ⋊ Γ as its unique Cartan subalgebra, up to unitary conjugacy.
Journal ArticleDOI
2-Local derivations and automorphisms on B(H)
TL;DR: In this article, it was shown that every 2-local derivation on the algebra B (H ) of all bounded linear operators on a Hilbert space H is a derivation.
Journal ArticleDOI
A fixed point theorem for L1 spaces
TL;DR: In this paper, a fixed point theorem for a family of Banach spaces for L^1 was proved for the derivation problem of group algebras, which was first introduced in the 1960s.
Journal ArticleDOI
SU(1,1) Lie algebraic approach to linear dissipative processes in quantum optics
TL;DR: In this paper, an SU(1, 1) Lie algebraic formulation is presented for investigating the linear dissipative processes in quantum optical systems, which is used for investigating a dissipative nonlinear oscillator, the quantum mechanical model of phase modulation, and the photon echo in the localized electron-phonon system.