The invariant subspace problem and Rosenblum operators
报告专家：张远航（吉林大学）
报告时间：12月16日（星期二）下午15:00-16:00
报告地点：觅讯视频会议ID：71751104 密码：1234
报告摘要：
Let T ∈ B(H) be an invertible operator. From the 1940’s, Gelfand, Hille and Wermer investigated the invariant subspaces of T by analyzing the growth of ||T^n ||, where n ∈ Z. In this talk, we study the invariant subspaces of T by estimating the growth of ||T^n + λT^{-n}||, where n ∈ N and λ is a nonzero complex constant. The key ingredient of our approach is introducing the notion of shift representation operators, which is based on the Rosenblum operators. In addition, by employing shift representation operators, we provide an equivalent of the Invariant Subspace Problem via the injectivity of certain Hankel operators. If time permits, we will show that every operator with the ideal property has a non-trivial invariant subspace. This is a joint work with Junsheng Fang, Bingzhe Hou and Chunlan Jiang.
专家简介：
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.及被Canad. J. Math.录用。
邀请人：余佳洋
