Linear maps of $\mathcal {C}^{\ast }$-algebras preserving the absolute value
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- by L. Terrell Gardner PDF
- Proc. Amer. Math. Soc. 76 (1979), 271-278 Request permission
Abstract:
In order that a linear map of ${\mathcal {C}^\ast }$-algebras $\phi :\mathcal {A} \to \mathcal {B}$ preserve absolute values, it is necessary and sufficient that it be 2-positive and preserve zero products of positive elements: if x and y are positive in $\mathcal {A}$, with $xy = 0$, then $\phi (x)\phi (y) = 0$. The generalized Schwarz inequalities of Kadison and Choi are extended to the nonunital case.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 271-278
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0537087-0
- MathSciNet review: 537087