Characterizations of 𝑤*-homomorphisms and expectations

Palmer, T. W.

doi:10.1090/S0002-9939-1974-0361804-1

Characterizations of $w\sp{\ast}$ -homomorphisms and expectations

Author: T. W. Palmer
Journal: Proc. Amer. Math. Soc. 46 (1974), 265-272
MSC: Primary 46K99
DOI: https://doi.org/10.1090/S0002-9939-1974-0361804-1
MathSciNet review: 0361804
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Abstract: If $\mathfrak{A}$ and $\mathfrak{B}$ are $\ast$ -algebras a map $\phi :\mathfrak{A} \to \mathfrak{B}$ is called a Schwarz map if it is linear and satisfies the Cauchy-Schwarz inequality $\phi {(a)^ \ast }\phi (a) \leq \phi (a ^\ast a)$ for all $a \in \mathfrak{A}$ . Under mild restrictions on $\mathfrak{A}$ and $\mathfrak{B}$ , $\ast$ -homomorphisms and expectations are characterized in terms of Schwarz maps $\phi :\mathfrak{A} \to \mathfrak{B}$ . The proofs are based on an elementary result on the multiplicative properties of Schwarz maps.

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