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Proceedings of the American Mathematical Society

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A dilation theorem for $ \cdot $-preserving maps of $ \mathcal{C}^*$-algebras


Author: L. Terrell Gardner
Journal: Proc. Amer. Math. Soc. 73 (1979), 341-345
MSC: Primary 46L05
MathSciNet review: 518516
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Abstract: A linear map of a (unital) $ {\mathcal{C}^\ast}$-algebra into a $ {\mathcal{C}^\ast}$-algebra, which preserves the absolute value, is analyzed as the composition of a (unital) $ ^\ast$-homomorphism into a usually larger target algebra, followed by a suitable multiplication $ x \mapsto xb = {b^{1/2}}x{b^{1/2}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0518516-5
Keywords: $ {\mathcal{C}^\ast}$-algebra, positive map, absolute value, dilation
Article copyright: © Copyright 1979 American Mathematical Society