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活动名称：所有酉算子都是3循环的，多数是2循环的

时 间：2026年3月27日15:50-16:30

地 点：重庆国家应用数学中心 308

主讲 人：张远航 教授

主办单位：数学科学学院

主讲人简介：

张远航，吉林大学数学学院教授，研究方向为算子理论和算子代数，目前主要研究兴趣是线性算子的结构、单核C*-代数分类、套代数的可逆元群连通性问题。研究成果发表于J. Funct. Anal.、J. Noncommut. Geom.、J.Operator Theory、Math. Z.、Proc. Amer. Math. Soc.、Sci.China Math.、Studia Math.和Canad. J. Math.等知名数学期刊。

活动简介：

Let H be a complex, separable Hilbert space (of finite or infinite dimension), and let U(H) denote the group of unitary operators on H. In the finite-dimensional setting, we prove that every unitary operator of determinant one can be expressed as the product of two operators, each unitarily equivalent to the n × n unitary cycle. In the infinite-dimensional setting, we prove that every unitary operator U is a product of three operators, each unitarily equivalent to the bilateral shift, and if the spectrum of U has nonzero Lebesgue measure, then U is a product of two operators, each unitarily equivalent to the bilateral shift. This work is joint with Laurent Marcoux, Matja?Omladi?and Heydar Radjavi.