Extreme points in quotients of Hardy spaces

Abstract

In the Hardy spaces \(H^1\) and \(H^\infty \), there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems when \(H^1\) (resp., \(H^\infty \)) gets replaced by the quotient space \(H^1/E\) (resp., \(H^\infty /E\)), under certain assumptions on the subspace E. In the \(H^1\) setting, we also treat the case where the underlying space is taken to be the kernel of a Toeplitz operator.