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The last equivalence of the display in the proof of Theorem 2.2 (page 301) is not correct (and b ∈ A is missing inside the brackets of the fourth line of this display). As noted at the beginning of this section, A has a natural O-module structure defined by α.λ(a) = λ(a.α), λ.α(a) = λ(α.a) (α ∈ O, a ∈ A, λ ∈ A). We need to modify Definition 2.1 as follows. Definition 2.1 A is called module Arens regular (as an O-module) if the operator R λ : A → A ; a → a.λ is weakly compact for any λ ∈ A satisfying λ(α.ab) = Communicated by Jerome A. Goldstein.

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