Characterizations of $w^{\ast }$-homomorphisms and expectations
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- by T. W. Palmer PDF
- Proc. Amer. Math. Soc. 46 (1974), 265-272 Request permission
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.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- 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