Locally closedness of unbounded derivations in 𝐶*-algebras

Ôta, Shôichi

doi:10.1090/S0002-9939-1978-0487474-3

Locally closedness of unbounded derivations in $C^*$-algebras
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by Shôichi Ôta

Proc. Amer. Math. Soc. 71 (1978), 222-226

DOI: https://doi.org/10.1090/S0002-9939-1978-0487474-3

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Abstract:

We study a local property of unbounded derivations in ${C^ \ast }$-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 ${C^ \ast }$-subalgebra generated by a and the identity is contained in the domain.

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