Let M be a semifinite von Neumann algebra equipped with a
semifinite normal faithful trace τ. Let d be an injective positive
measurable operator with respect to (M,τ) such that d−1 is
also measurable. Define
Lp(d)=x∈L0(M):dx+xd∈Lp(M)and∥x∥Lp(d)=∥dx+xd∥p. We show that for 1\le p_0,
0<θ<1 and α0≥0,α1≥0 the interpolation equality
(Lp0(dα0),Lp1(dα1))θ=Lp(dα) holds with equivalent norms, where
p1=p01−θ+p1θ and
α=(1−θ)α0+θα1.Comment: To appear in Houston J. Mat