Orthogonality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules
Orthogonality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules
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DOI：
10.1016/j.jfa.2010.10.009
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
M. Frank;A. Mishchenko;A. Pavlov
中科院分区：
文献类型：
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作者：
M. Frank;A. Mishchenko;A. Pavlov
研究了满Hilbert C <$-模上的保正交正规、C <$-共形和共形模映射，得到了它们的一般结构.保极性有界模映射T充当与系数的C λ-代数的乘子代数的中心的元素λ的乘法，该乘子代数与等距模算子组合，只要特定元素λ的某些极分解条件在该乘子代数内满足。一般来说，T总是满足等式T（x），T（y）=| λ| 2 <$x，y <$对于Hilbert C <$-模的任何元素x，y。相反，C保形和保形有界模映射仅是等距模算子的正真实的倍数。
We investigate orthonormality-preserving, C⁎-conformal and conformal module mappings on full Hilbert C⁎-modules to obtain their general structure. Orthogonality-preserving bounded module maps T act as a multiplication by an element λ of 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 λ are fulfilled inside that multiplier algebra. Generally, T always fulfills 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 module maps are shown to be only the positive real multiples of isometric module operators.