论文标题
jordan $*$ - 连续地图上的同构，以$ c^{*} $ - 代数为代数
Jordan $*$-homomorphisms on the spaces of continuous maps taking values in $C^{*}$-algebras
论文作者
论文摘要
令$ \ mathcal {a} $为Unital $ c^{*} $ - 代数。我们认为Jordan $*$ - $ C（x，\ Mathcal {a}）$和Jordan $*$ - 同构$ \ operatatorName {lip}（x，x，x，\ mathcal {a}）$上的同构$ - 更准确地说，对于任何Unital $ c^{*} $ - 代数$ \ Mathcal {a} $，我们证明了$ c（x，x，\ nathcal {a}）$的每个jordan $*$ - 同型 - 同型 - 同型$*$*$*$ - y-yourphismist ot $ \ \ \ operatornornearnearnearmeanemeanemearnearmeanmeanemearneansameAnsameAnemememeanememememeane} $ rip}使用$ \ Mathcal {a} $的不可约表示的加权构图运算符。此外，当$ \ MATHCAL {A} _1 $和$ \ MATHCAL {A} _2 $是原始$ C^{*} $ - 代数时，我们表征了Jordan $*$ - 同构。这些结果统一并丰富了$ c（x，\ mathcal {a}）$和$ \ operatorAtorname {lip}（x，x，x，x，\ nathcal {a}）$的$ c（x，\ nathcal {a}）上的同构的先前作品。
Let $\mathcal{A}$ be a unital $C^{*}$-algebra. We consider Jordan $*$-homomorphisms on $C(X, \mathcal{A})$ and Jordan $*$-homomorphisms on $\operatorname{Lip}(X,\mathcal{A})$. More precisely, for any unital $C^{*}$-algebra $\mathcal{A}$, we prove that every Jordan $*$-homomorphism on $C(X, \mathcal{A})$ and every Jordan $*$-homomorphism on $\operatorname{Lip}(X,\mathcal{A})$ is represented as a weighted composition operator by using the irreducible representations of $\mathcal{A}$. In addition, when $\mathcal{A}_1$ and $\mathcal{A}_2$ are primitive $C^{*}$-algebras, we characterize the Jordan $*$-isomorphisms. These results unify and enrich previous works on algebra $*$-homomorphisms on $C(X, \mathcal{A})$ and $\operatorname{Lip}(X,\mathcal{A})$ for several concrete examples of $\mathcal{A}$.
