ar X iv : m at h / 05 08 02 8 v 1 [ m at h . FA ] 1 A ug 2 00 5 AUTOMATIC CONTINUITY OF σ - DERIVATIONS ON C ∗ - ALGEBRAS
نویسنده
چکیده
Let A be a C-algebra acting on a Hilbert space H, σ : A → B(H) be a linear mapping and d : A → B(H) be a σ-derivation. Generalizing the celebrated theorem of Sakai, we prove that if σ is a continuous ∗-mapping then d is automatically continuous. In addition, we show the converse is true in the sense that if d is a continuous ∗-σ-derivation then there exists a continuous linear mapping Σ : A → B(H) such that d is ∗-Σ-derivation. The continuity of the so-called ∗-(σ, τ)-derivations is also discussed.
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