《一些Kadison-Singer代数的例子》是于嘉琪、李建奎撰写的一篇论文。论文摘要 设H是一个复的Hilbert空间。L={(0),L,M,K,H}是一个五角子空间格,满足M是L和x0的闭线性扩张,其中非零元x0属于K┴但不属于K+L。本文证明了Alg L是一个半单的Kadison-Singer代数。同时还给出两个不是套代数的CSL代数的例子,一...
设LL为无限维可分Hilbert空间HH上的套NN和秩一投影PξPξ所生成的完备格, 其中PξPξ表示HH到非零向量ξξ生成一维子空间上的正交投影. 假设ξξ为由NN生成的von Neumann代数N′′N″的分离向量, 本文证明LL是个Kadison-Singer格, 从而相应的不变子空间格代数Alg(L)Alg(L)是个Kadison-Singer代数. 此外, ...
Kadison-Singer algebras, I:Hyperfinite case. L. Ge,W. Yuan. Proceedings of the National Academy of Sciences of the United States of America . 2010Limin Ge,Wei Yuan.Kadison-Singer algebras. I: Hyperfinite case.Proceedings of the National Academy of Sciences of the United States of America. ...
本文研究Kadison-Singer格的结构和强Kadison-Singer代数的构造,证明有限维Hilbert空间上的有限Kadison-Singer格不包含非平凡的约化投影,并且在无限维可分Hilbert空间的n重直和上构造了一类强Kadison-Singer代数.作为推论,本文给出了存在两个Kadison-Singer代数其斜积是一个强Kadison-Singer代数的例子.关键...
Kadison-Singer格矩阵代数Kadison-Singer代数von Neumann代数Kadison-Singer LatticeMatrix AlgebraKadison-Singer Algebravon Neumann Algebralt;span style=font-family:宋体;font-size:10pt;gt;本文在矩阵代数Mlt;span style=font-family:Times New Roman,serif;font-size:12pt;gt;lt;subgt;2lt;/subgt;(C)lt;/...
Recently Marcus, Spielman and Srivastava gave a spectacular proof of a theorem which implies a positive solution to the Kadison-Singer problem via Weaver's $KS_r$ conjecture. We extend this theorem to the realm of hyperbolic polynomials and hyperbolicity cones, as well as to arbitrary ranks. We...
We use the method of interlacing families of polynomials to prove Weaver's conjecture KS2, which is known to imply a positive solution to the Kadison-Singer problem via Anderson's Paving Conjecture. Our proof goes through an analysis of the largest roots of a family of polynomials that we ...
Ren, Y., Wu, W.: Some new classes of Kadison-Singer lattices in Hilbert spaces. Sci. China, Ser. A , acceptedYuanHong Ren,WenMing Wu.Some new classes of Kadison-Singer lattices in Hilbert spaces[J]. Science China Mathematics .2014(4)...
Kadison-Singer问题 Kadison-Singer问题,专业术语。2022年9月23日,丹尼尔·斯皮尔曼凭借Kadison-Singer问题等方面的研究,荣获“2023年数学突破奖 ”。2022年9月23日,来自耶鲁大学的丹尼尔·斯皮尔曼(Daniel A. Spielman),凭借Kadison-Singer问题等方面的研究,荣获“2023年数学突破奖 ”。