THE DUAL OF NONCOMMUTATIVE H-1

Let M be a von Neumann algebra with a faithful normal tracial state ta u and let H-infinity be a finite maximal subdiagonal subalgebra of M. In previous work we defined a harmonic conjugate relative to H-infinit y. Let H-1 be the closure of H-infinity in the noncommutative Lebesgue space L-1(M). By analysing the behaviour of the harmonic conjugate in L-1(M), we identify the dual space of H-1 as a concrete space of oper ators.