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数学与信息科学学院系列学术报告

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讲座题目:数学与信息科学学院系列学术报告
讲座人: Don Hadwin教授、刘文静博士
讲座时间:10:00
讲座日期:2017-8-14
地点:数学与信息科学学院学术报告厅

讲座题目1:Approximate unitary equivalence in a von Neumann algebra

讲座时间:10:00-11:00

报告人:Don Hadwin教授

讲座内容简介:

In 1976, D. Voiculescu gave a very beautiful characterization of the approximate unitary equivalence of unital representations of a separable unital C*-algebra into the algebra of operators on a separable Hilbert space.  Later I gave a different characterization completely in terms of rank.  More recently Huiru Ding and I generalized some of these results for representations into a von Neumann algebra.  Recently, in joint work with Shi Rui, we extended some of Voiculescu's results with respect to the "compact" operators on a II_infinity factor.

讲座人简介:

        Don Hadwin,美国新罕布什尔大学数学与统计学院终身教授。Hadwin 教授于1975年毕业于美国印第安纳大学,师从著名算子论专家Paul Halmos。毕业后先后在美国夏威夷大学,美国新罕布什尔大学长期从事泛函分析,算子理论与算子代数的研究工作,研究成果卓著, 在《Journal of Functional Analysis》,《Transactions of the American Mathematical Society》,《Journal of Operator Theory》,《Journal of Algebra》,《The Bulletin of the London Mathematical Society》,《Integral Equations and Operator Theory》等国际刊物上发表论文160余篇。

 

讲座题目2:An extension of the Beurling-Chen-Hadwin-Shen theorem for noncommutative Hardy spaces associated with finite von Neumann algebras

讲座时间:11:00-12:00

报告人:刘文静博士

讲座内容简介:

    In 2015, Yanni Chen, Don Hadwin and Junhao Shen proved a noncommutative version of Beurling's theorem for a continuous unitarily invariant norm α on a tracial von Neumann algebra (M, τ) such that α is one-norm dominating with respect to τ. The role of H infinity is played by a maximal subdiagonal algebra A . In the talk, we first show that if α is a continuous normalized unitarily invariant norm on (M, τ), then there exists a faithful normal tracial state ρ on M and a constant c >0 such that α is a c times one-norm dominating norm on (M, ρ). Moreover, ρ(x) = τ(xg), where x in M, g is positive in L1(Z(M)), where Z(M) is the center of M . Here c and ρ are not unique. However, if there is a c and ρ so that the Fuglede-Kadison determinant of g is positive, then Beurling-Chen-Hadwin-Shen theorem holds for L^α(M, τ). The key ingredients in the proof of our result include a factorization theorem and a density theorem for L^ α(M, ρ).

讲座人简介:

   刘文静,2013年硕士毕业于陕西师范大学数学与信息科学学院,现为美国新罕布什尔大学数学与统计学院在读博士。研究方向包括算子理论和算子代数以及非交换Hardy空间理论。

 
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陕西师范大学数学与信息科学学院