Resumen de On the relationships between Hp (T, X/Y) and Hp (T, X) - Hp (T, Y)

Artur Michalak

• First we show that for every $1\leq p ?\infty$ the space $H^p(\mathbb{T}, L^1(\lambda)/H^1)$ cannot be naturally identified with $H^p(\mathbb{T}, L^1(\lambda))/H^p(\mathbb{T},H^1)$. Next we show that if $Y$ is a closed locally complemented subspace of a complex Banach space $X$ and $0 ? p ?\infty$, then the space $H^p(\mathbb{T},X/Y )$ is isomorphic to the quotient space $H^p(\mathbb{T},X)/H^p(\mathbb{T}, Y )$. This allows us to show that all odd duals of the James Tree space $JT_2$ have the analytic Radon-Nikodym property.