On multipliers and order-bounded operators in 𝐶*-algebras

Andersen, Tage Bai

doi:10.1090/S0002-9939-1970-0261364-6

On multipliers and order-bounded operators in $C^{\ast }$-algebras
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by Tage Bai Andersen

Proc. Amer. Math. Soc. 25 (1970), 896-899

DOI: https://doi.org/10.1090/S0002-9939-1970-0261364-6

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Abstract:

It is shown that the selfadjoint multipliers from a sub-${C^{\ast }}$-algebra to the bigger ${C^{\ast }}$-algebra are exactly the order-bounded operators. As a corollary we get a characterization of the relative commutant of a sub-${C^{\ast }}$-algebra with unit.

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