Time: Tuesday, Sept 20, 2016, 2:00pm @ MTH1311

Speaker: Prof. Sivaram Narayan (Central Michigan University)

Title: Complex Symmetric Composition Operators on the Hardy Space

Abstract: We say that a bounded operator T on a complex Hilbert space H is complex symmetric if there exists a conjugation (i.e., a conjugate linear, isometric involution) J such that T=JT^*J. In this talk, we will first discuss a few general results about complex symmetric operators on a Hilbert space. We will then focus for most of the talk on the complex symmetry of composition operators C_\varphi f = f \circ \varphi induced on the Hardy space H^2 by analytic self-maps \varphi of the open unit disk D. We show that there are complex symmetric composition operators on H^2 induced by \varphi that are linear-fractional but not automorphisms. In doing so, we answer a recent question of Noor, and partially answer the original problem posed by Garcia and Hammond. Back to seminar