Strong singularity for subfactors
نویسندگان
چکیده
منابع مشابه
Strong Singularity for Subfactors
We examine the notion of α-strong singularity for subfactors of a II1 factor, which is a metric quantity that relates the distance between a unitary in the factor and a subalgebra with the distance between that subalgebra and its unitary conjugate. Through planar algebra techniques, we demonstrate the existence of a finite index singular subfactor of the hyperfinite II1 factor that cannot be st...
متن کاملStrong Singularity for Subfactors of a II 1 Factor
We examine the notion of α-strong singularity for subfactors of a II1 factor, which is a metric quantity that relates the distance of a unitary to a subalgebra with the distance between that subalgebra and its unitary conjugate. Using work of Popa, Sinclair, and Smith, we show that there exists an absolute constant 0 < c < 1 such that all subfactors are c-strongly singular. Under additional hyp...
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We study L-Betti numbers for von Neumann algebras, as defined by D. Shlyakhtenko and A. Connes in [1], in the presence of a bi-finite correspondence and proof a proportionality formula.
متن کاملStrong Singularity of Singular Masas in Ii 1 Factors Allan
A singular masa A in a II1 factor N is defined by the property that any unitary w ∈ N for which A = wAw∗ must lie in A. A strongly singular masa A is one that satisfies the inequality ‖EA − EwAw∗‖∞,2 ≥ ‖w − EA(w)‖2 for all unitaries w ∈ N , where EA is the conditional expectation of N onto A, and ‖ · ‖∞,2 is defined for bounded maps φ : N → N by sup{‖φ(x)‖2 : x ∈ N, ‖x‖ ≤ 1}. Strong singularity...
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&stMCt-In an exploratory paper, T. Berger studied discrete random proceases which generate information slower than linearly with time. One of his objectives was to provide a physically meaningful definition of a deterministic process, and to this end he introduced the notion of strong information singularity. His work is supplemented by demonstrating that a large class of convariance stationary...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2010
ISSN: 0024-6093
DOI: 10.1112/blms/bdp137