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Range preserving maps between the spaces of continuous functions with values in a locally convex space
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-09 , DOI: 10.1090/proc/15108
Yuta Enami

Abstract:Let $ C(X,E)$ be the linear space of all continuous functions on a compact Hausdorff space $ X$ with values in a locally convex space $ E$. We characterize maps $ T:C(X,E)\to C(Y,E)$ which satisfy $ \mathrm {Ran}(TF-TG)\subset \mathrm {Ran}(F-G)$ for all $ F,G\in C(X,E)$.


中文翻译:

具有局部凸空间中的值的连续函数的空间之间的范围保留映射

摘要:设$ C(X,E)$紧凑型Hausdorff空间上所有连续函数的线性空间,$ X $其值在局部凸空间内$ E $。我们刻画了所有人都满意的地图。 $ T:C(X,E)\至C(Y,E)$ $ \ mathrm {Ran}(TF-TG)\ subset \ mathrm {Ran}(FG)$ $ F,G \ in C(X,E)$
更新日期:2020-11-12
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