**Speaker**: Monojit Bhattacharjee

**Date**: 31 March, 2015 (Tuesday)

**Time**: 09:15 pm – 10:15 pm

**Venue**: Lecture Hall I, Department of Mathematics

**Abstract**:

In this talk we will present to you the proof of the “Beurling-Lax-Halmos” theorem. Let be a contraction on a Hilbert space and be a non-trivial closed subspace of . We prove that is a -invariant subspace of if and only if there exists a Hilbert space and a partial isometric operator such that and = ran . As a corollary of this theorem we will prove the “Beurling-Lax-Halmos” theorem. This theorem characterizes the shift-invariant subspaces of the vector-valued Hardy space.

**Area**: Functional Analysis, Operator Theory