On multipliers and order-bounded operators in $C^{\ast }$-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 | References | Similar Articles | Additional Information
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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- Jacques Dixmier, Les $C^{\ast } $-algèbres et leurs reprĂŠsentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Ăditeur-Imprimeur, Paris, 1964 (French). MR 0171173
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Additional Information
Keywords:
Multiplier,
order-bounded operator,
relative commutant
Article copyright:
© Copyright 1970
American Mathematical Society