Abstract
It is proved that the monotone σ-closure of the self-adjoint part of anyC*-algebraA is the self-adjoint part of aC*-algebra ℬ. IfA is of type I it is proved that ℬ is weakly σ-closed, i.e. ℬ is aΣ*-algebra. The physical importance ofΣ*-algebras was explained in [1] and [7].
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Pedersen, G.K. On weak and monotone σ-closures ofC*-algebras. Commun.Math. Phys. 11, 221–226 (1969). https://doi.org/10.1007/BF01645808
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DOI: https://doi.org/10.1007/BF01645808