Abstract
Under certain additional assumptions, it is proved that a w∗-closed subalgebra X of L∞(μ) (more generally, a w∗-closed module over X) verifies the Grothendieck theorem. The assumptions in question imitate a property of the classical harmonic conjugation operator but are less restrictive than it is usual in similar settings. Specifically, μ may fail to be multiplicative on X, etc.
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