Abstract
In the author's previous paper, he constructed a complex one-parameter family of non-commutative Lp-spaces [Formula: see text], [Formula: see text], 1 < p < ∞, for a von Neumann algebra ℳ with respect to a fixed faithful normal semi-finite weight φ on ℳ by using Calderón's complex interpolation method. In this paper, we will construct bounded non-degenerate bilinear forms < , >p,(α) on [Formula: see text], [Formula: see text], 1 < p <∞, 1/p + 1/q = 1, and bounded non-degenerate sesquilinear forms ( | )p,(α) on [Formula: see text], [Formula: see text], 1 < p < ∞, 1/p + 1/q = 1, and by using general theory of the complex interpolation method we show the reflexivity of [Formula: see text] and the duality between [Formula: see text] and [Formula: see text] via < , >p,(α) (or the duality between [Formula: see text] and [Formula: see text] via ( | )p,(α)). Moreover, we discuss bimodule properties of [Formula: see text].
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