Complex interpolation of weighted noncommutative $L_p$-spaces

Details Complex interpolation of weighted noncommutative $L_p$-spaces Complex interpolation of weighted noncommutative $L_p$-spaces

2009-06-29

arxiv.org/abs/0906.5305v2

Mathematics

Operator Algebras

To appear in Houston J. Math

Scientific paper

Let $\mathcal{M}$ be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace $\tau$. Let $d$ be an injective positive measurable operator with respect to $(\mathcal{M}, \tau)$ such that $d^{-1}$ is also measurable. Define $$L_p(d)={x\in L_0(\mathcal{M}) : dx+xd\in L_p(\mathcal{M})}\quad{and}\quad \|x\|_{L_p(d)}=\|dx+xd\|_p .$$ We show that for $1\le p_0

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