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In order that a linear map of 6'-algebras «¡>: & -» ® 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 &, with xy 0, then <&x)$(y) = 0. The generalized Schwarz inequalities of Kadison and Choi are extended to the nonunital case.

Linear maps of 𝒞*-algebras preserving the absolute value