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Chilin","submitted_at":"2012-05-28T11:38:48Z","abstract_excerpt":"Let $\\mathcal{A}$ be a commutative $AW^*$-algebra, let $S(\\mathcal{A})$ be the *-algebra of all measurable operators affiliated with $\\mathcal{A}$, let $\\mathcal{I}$ be an ideal in $\\mathcal{A}$, let $s(\\mathcal{I})$ be the support of the ideal $\\mathcal{I}$ and let $\\mathbb{Y}$ be a solid subspace in $S(\\mathcal{A})$. The necessary and sufficient conditions of existence of non-zero band preserving derivations from $\\mathcal{I}$ to $\\mathbb{Y}$ are given. 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