Real-linear surjective isometries between function spaces
Real-linear surjective isometries between function spaces
复制标题
函数空间之间的实线性满射等距
DOI：
10.1016/j.topol.2017.05.002
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Kazuhiro Kawamura and Takeshi Miura
中科院分区：
文献类型：
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作者：
H. Tanaka;Kazuhiro Kawamura and Takeshi Miura
研究了包含所有常值函数的连续函数的子空间之间的满射等距，并讨论了其基本空间的点的分离。在许多情况下，每一个这样的等距都是由加权复合算子和它的复共轭的组合表示的，称为标准形，而存在一个不采取这种形式的等距（[14]）。本文在紧Hausdorff空间上寻找一个拓扑条件，使得空间上的函数空间的满射等距具有标准形。我们还推广了[14]的构造，证明了：如果紧致可度量化空间X允许具有整体截面的圆群的半自由作用，则X上存在不取标准形的函数空间的等距。
We study surjective isometries between subspaces of continuous functions containing all constant functions and separating the points of the underlying spaces. In many contexts, every such isometry is represented by a combination of a weighted composition operator and its complex conjugate, called the canonical form, while there exists an isometry which does not take such a form ([14]). We seek a topological condition on compact Hausdorff spaces such that every surjective isometry on function spaces over the spaces has the canonical form. Also we extend the construction of [14] to show that, if a compact metrizable spaceXadmits a semi-free action of the circle group with a global section, then there exists an isometry of a function space onXwhich does not take the canonical form.