Hilbert C*-模上保持正交性、C*-共形与共形模映射
Orthogonality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules
AI总结：
本文研究Hilbert C*-模上保持正交性、C*-共形与共形模映射的结构，证明前者为乘子代数中心元素与等距模算子的复合，后者仅为等距模算子的正实数倍。
摘要：
我们研究Hilbert C*-模上保持正交性、C*-共形与共形模映射，以获取其一般结构。保持正交性的有界模映射T的作用相当于乘以系数C*-代数的乘子代数中心的一个元素λ，并复合一个等距模算子，前提是在该乘子代数内满足特定元素λ的某些极分解条件。一般地，T对Hilbert C*-模中任意元素x,y总满足等式$<T(x),T(y) > = | λ|^2 < x,y>$。相反，C*-共形与共形有界C*-线性映射被证明仅为等距模算子的正实数倍。
英文摘要：
We investigate orthonormality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules to obtain their general structure. Orthogonality-preserving bounded module maps T act as a multiplication by an element λof the center of the multiplier algebra of the C*-algebra of coefficients combined with an isometric module operator as long as some polar decomposition conditions for the specific element λare fulfilled inside that multiplier algebra. Generally, T always fulfils the equality $<T(x),T(y) > = | λ|^2 < x,y>$ for any elements x,y of the Hilbert C*-module. At the contrary, C*-conformal and conformal bounded C*-linear mappings are shown to be only the positive real multiples of isometric module operators.
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