Jordan-morphisms in $\ast$-algebras
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- by Klaus Thomsen PDF
- Proc. Amer. Math. Soc. 86 (1982), 283-286 Request permission
Abstract:
As a continuation of Størmer’s work on Jordan-morphisms in $C*$-algebras we consider Jordan-morphisms $\varphi$ from $*$-algebras $\mathfrak {A}$ into the $*$-algebra $B(\mathcal {H})$, and assume that $\varphi (\mathfrak {A})$ is again a $*$-algebra. We then establish the existence of three mutually orthogonal central projections ${P_i}$, $i = 1,2,3$, in $\varphi {\left ( {} \right )^{\prime \prime }}$ such that ${P_1} + {P_2} + {P_3} = I$ and $\varphi ( \cdot ){P_1}$ is a morphism, $\varphi ( \cdot ){P_2}$ is an antimorphism. ${P_3}$ is the largest projection such that $\varphi ( \cdot ){P_3}$ is a morphism, as well as an antimorphism. Uniqueness is also shown. The theorem improves a result of Kadison and Størmer. Our proofs are self-contained.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 283-286
- MSC: Primary 46K05; Secondary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0667290-0
- MathSciNet review: 667290