Speaker: Dr. Amit Maji

Title of the Talk: Spectral Decomposition and Invariant Subspaces

Date, Time and venue: 3rd Oct, 2024 at 12:00PM, @Meeting Room, Dept of Mathematics.

About the Speaker: Dr. Amit Maji is currently working as Associate Professor at Indian Institute of Technology Roorkee. He has obtained, Ph.D from Indian Institute of Technology Kharagpur, Post Doctoral experience Indian Statistical Institute Bangalore Centre His research area is Operator Theory; Functional Analysis.

Abstract: The main aim of this talk is to discuss the structure of a certain class of bounded linear operators on Hilbert spaces. In the first half of this talk, we shall cover the spectral theory for normal matrices and normal operators on Hilbert spaces. After that, we describe the Wold decomposition and analytic model for a single isometry and then discuss the existence of Wold decomposition for n-tuples of isometries. Finally, we talk about the Beurling’s theorem for shift invariant subspaces of Hardy space over the unit open disc as well as Hardy space over the polydisc.