Embedding normed linear spaces into $C(X)$
نویسندگان
چکیده مقاله:
It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can indeed be chosen to be the Stone--Cech compactification of $L^*setminus{0}$, where $L^*setminus{0}$ is endowed with the supremum norm topology.
منابع مشابه
embedding normed linear spaces into $c(x)$
it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$. here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology, which is compact by the banach--alaoglu theorem. we prove that the compact hausdorff space $x$ can ...
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عنوان ژورنال
دوره 43 شماره 1
صفحات 131- 135
تاریخ انتشار 2017-02-22
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