Abstract

We study a local property of unbounded derivations in C ∗ {C^ \ast } -algebras, introducing locally closedness for derivations. We show that a derivation is locally closed and the positive portion of the domain is closed under the square root operation if and only if for each hermitian element a in the domain the C ∗ {C^ \ast } -subalgebra generated by a and the identity is contained in the domain.

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