Hilbert Modules in Analytic Function Spaces

2017-3-6 11:26:10 1149


The Invariant Subspace Problem is the most well-known unsolved problem in Operator Theory. For normal operators, the spectral decomposition theorem completely describes the structure of their invariant subspaces. For non-normal operators, a fundamental example is the unilateral shift operator S on a Hilbert space. In 1949, Beurling gave a complete description of its invariant using analytic function theory in the setting of classical Hardy space H2(D): a closed subspace M⊂H2(D) is invariant for S if and only if M = θH2(D) for some inner function θ. This settlement relies on additional structures of analytic function space: multiplication, boundedness and boundary values of analytic functions. These structures are not available in general Hilbert spaces. Beurling’s theorem not only suggested a good approach to Invariant Subspace Problem but also became a foundation for many other developments in Operator Theory.

A great amount of work has been done to search for generalizations of Beurling’s idea. Now the theory has grown much beyond the scope of invariant subspace problem. This workshop aims to bring together experts to report and exchange ideas on recent developments.


Organizers

NameUniversity
Ronald DouglasTexas A&M, USA
Kunyu GuoFudan University, China
Gadadhar MisraIndian Institute of Science
Rongwei YangSUNY at Albany, USA


Participants


Shibananda BiswasIndian Institute of Science Education Research, Kolkata
Guangfu CaoGuangzhou University, China
Sameer ChavanIndian Institute of Technology, Kanpur
Li ChenTianjin University, China
Xiaoman ChenFudan University, China
Ronald G. DouglasTexas A&M, USA
Yongjiang DuanNortheast Normal University, China
Miroslav EnglisDepartment of Mathematics, Silesian University, Czech Republic
Quanlei FangBronx Community College, New York, USA
Xiang FangNational Central University, Taiwan
Soumitra GharaIndian Institute of Science, Bangalore
Kunyu GuoFudan University, China
Rajeev GuptaIndian Institute of Technology, Kapur
Somnath HazraIndian Institute of Science, Bangalore, India
Wei HeSoutheast University, China
Jinchuan HouTaiyuan University of Technology, China
Shengzhao HouSuzhou University, China
Junyun HuJiaxing University, China
Hansong HuangEast China University of Science and Technology, China
Keiji IzuchiDepartment of Mathematics, Niigata University, Japan
Kouhei IzuchiDepartmet of Mathematics, Yamaguchi University, Japan
Guoxing JiShanxi Normal University, China
Kui JiHebei Normal University, China
Youqing JiJilin University, China
Chunlan JiangHebei Normal University, China
Laszlo KerchyBolyai Institute, University of Szeged, Hungary
Dinesh Kumar KeshariIndian Statistical Institute, Bangalore
Surjit KumarIndian Institute of Science, Bangalore
Hyun-Kyoung KwonDepartment of Mathematics, University of Alabama, USA
Wing-Suet LiDepartment of Mathematics, Georgia Institute of Technology, USA
Constanze Dong-Li LiawDepartment of Mathematics, Baylor University, USA
Yufeng LuDalian University of Technology, China
Shuaibing LuoHunan University, China
Gadadhar MisraIndian Institute of Science
Avijit PalIndian Institute of Science Education Research, Kolkata
Marek PtakDepartment of Mathematics, Uniwersytet Rolniczy, Krakow, Poland
Yueshi QinChongqing University, China
Mohammed Ramiz RezaIndian Institute of Science, Bangalore
Subrata Shyam RoyIndian Institute of Science Education Research, Kolkata
Jaydeb SarkarIndian Statistical Institute, Bangalore
Michio SetoNational Defense Academy, Yokosuka 239-8686, Japan
Shnhua SunJiaxing University, China
Shailesh TrivediHarish-Chandra Research Institute Allahabad, India
Harald Ernst Otto UpmeierUniversity of Marburg, Germany
Cherian VarugheseRenaissance Communications, Bangalore, Indian
Kai WangFudan University, China
Penghui WangShandong Univeristy, China
Xiaofeng WangGuangzhou University, China
Zipeng WangShanxi Normal University, China
Junde WuZhejiang University, China
Yue WuCentral University of Finance and Economics, China
Jingbo XiaDepartment of Mathematics, SUNY at Buffalo, NY, USA
Xianmin XuJiaxing University, China
Congquan YanJiaxing University, China
Rongwei YangSUNY at Albany, USA
Yixin YangDalian University of Technology, China
Jiayang YuSichuan University, China
Cong ZhaoShandong University, China
Dechao ZhengDepartment of Mathematics, Vanderbilt University, USA
Sen ZhuJilin University, China