Duality and interpolation for symmetric Banach spaces of noncommutative quasi-martingales

摘要

Let E be a symmetric Banach space with the Fatou property and 1 < pE <= qE < p. We prove the duality for symmetric Banach space (p)(E) over cap (M) which is a kind of noncommutative quasi-martingale space. As its applications, we discuss concrete description of the symmetric Banach space (p)(E) over cap (M) as interpolations of quasi-martingale L-p-spaces.