Mathematics Research Seminar Series: Toeplitz and Truncated Toeplitz Operators

In this talk, he will focus on operators defined on spaces of analytic functions on the open unit disc D = {z ∈ C : |z| < 1}. The main instincts are Hardy-Hilbert space, model spaces and their operators. Model spaces are backward shift invariant subspaces of H2 (Hardy-Hilbert space).

Truncated Toeplitz operators are compression of multiplication operators to model spaces. Some of the algebraic properties of the truncated Toeplitz operators will be presented. Ultimately, he will generalize the whole theory to the vector-valued version.