Linear Analysis Seminar

Date: February 27, 2015

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Ron Douglas, Texas A&M University

Title: Applications of geometrical ideas to operator theory

Abstract: From Beurling's Theorem it follows that a cyclic invariant subspace M of a vector valued Hardy Space, H_ε²(D), is isometrically isomorphic to H²(D). For the Bergman space, L_a²(D), this fails miserably. We show, however, that if M is complimented in L_a,ε²(D) by an invariant subspace, then the result still holds. Along different lines we show that the operator-valued corona theorem for the unit disk fails, reproving a result of Trail which answers in the negative a conjecture of Nikolskii. Again, geometrical ideas are at the heart of the proof which rests on the fact that the Hardy and Bergman shifts are not similar.