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Proceedings of the American Mathematical Society

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On multipliers and order-bounded operators in $ C\sp{\ast} $-algebras


Author: Tage Bai Andersen
Journal: Proc. Amer. Math. Soc. 25 (1970), 896-899
MSC: Primary 46.65
DOI: https://doi.org/10.1090/S0002-9939-1970-0261364-6
MathSciNet review: 0261364
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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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DOI: https://doi.org/10.1090/S0002-9939-1970-0261364-6
Keywords: Multiplier, order-bounded operator, relative commutant
Article copyright: © Copyright 1970 American Mathematical Society