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The kernel spaces, Fredholmness and compact defect
时间:2020年11月30日 09:59 点击数:

报告人:李然

报告地点:腾讯会议

报告时间:2020年12月02日星期三09:00-10:00

邀请人:李宇飞

报告摘要:

In this talk, we study some conditions about invertible and Fredholm truncated Toeplitz operators which have unique symbols. Obviously, if the defect operator of truncated Toeplitz operator $A_f$ is compact, then $A_f$ is a Fredholm operator. In addtion, we provide the necessary and sufficient condition that the defect operator $I-A_f^*A_f$ of truncated Toeplitz operator $A_f$ for $f\in H^\infty$ with $\|f\|_\infty\leq1$ is of finite-rank on the model space $K_u^2$. Moreover, the necessary and sufficient condition is obtained for $I-A_f^*A_f$ with $f\in K_u^2\cap L^\infty$ to be compact on the model space $K_u^2$. For $f\in L^\infty$, we get the necessary and sufficient condition that the defect operator $I-A_f^*A_f$ of truncated Toeplitz operator $A_f$ meeting some conditions is compact on the model space $K_u^2$. Besides, we give some results about the kernel spaces of truncated Toeplitz operators.

会议网址:https://meeting.tencent.com/s/7SRDA480TIHE

会议ID;302 148 983

会议密码:654321

主讲人简介:

李然,辽宁师范大学数学学院讲师,硕士研究生导师。2018年毕业于大连理工大学数学科学学院,获得理学博士学位。主要研究算子理论与算子代数,具体包括函数空间理论及其空间上的算子理论、C*-代数和von Neumann 代数等。2019年获国家自然青年科学基金项目和辽宁省教育厅青年项目。近五年在SCI期刊共发表学术论文5篇。2020年入选辽宁省“百千万人才工程”万人层次。

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