Extreme points in quotients of Hardy spaces

Source abstract

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