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On Strong kadison–singer Algebras

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Acta Mathematica Sinica,English Series 2013年第12期29卷 2219-2232页

作者： Ai Ju DONG Dong WANG School of Mathematics and Computer Engineering Xi’an University of Arts and Science Institute of Mathematics Academy of Mathematics and Systems Science Department of Mathematics and Statistics University of New Hampshire

We show that many kadison-singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non... 详细信息

关键词： kadison-singer algebra kadison-singer lattice reflexive algebra double triangle lattice von Neumann algebra

Cohomology groups of a new class of kadison-singer algebras

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Science China Mathematics 2024年第3期67卷 593-606页

作者： Guangyu An Xing Cheng Jun Sheng School of Mathematics and Data Science Shaanxi University of Science and TechnologyXi’an 710021China

Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑^(∞)_(n=1)en/2n be a separating vector for the commutant N',E_(ξ)be the projection from H onto the subspace[Cξ]spanned by the vectorξ,and Q be the projection from K=H⊕H⊕H onto the closed subspace{(η,η,η)^(T):η∈H}.Suppose that L is the projection lattice generated by the projections(E_(ξ) 0 0 0 0 0 0 0 0),{(E 0 0 0 0 0 0 0 0):E∈N},(I 0 0 0 I 0 0 0 0) and *** show that L is a kadison-singer lattice with the trivial ***,we prove that every n-th bounded cohomology group H~n(AlgL,B(K))with coefficients in B(K)is trivial for n≥1.

关键词： kadison-singer algebra kadison-singer lattice derivation cohomology group

On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice

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Science China Mathematics 2015年第11期58卷 2373-2386页

作者： DONG AiJu WANG Dong School of Mathematics and Computer Engineering Xi'an University of Arts and Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Department of Mathematics and Statistics University of New Hampshire

We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix *** a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).

关键词： kadison-singer algebra kadison-singer lattice reflexive algebra double triangle lattice factorof type II1