%0 Journal Article
%T Embedding normed linear spaces into $C(X)$
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Fakhar, M.
%A Koushesh, M. R.
%A Raoofi, M.
%D 2017
%\ 02/22/2017
%V 43
%N 1
%P 131-135
%! Embedding normed linear spaces into $C(X)$
%K Stone-Cech compactification
%K Banach-Alaoglu theorem
%K embedding theorem
%R
%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 indeed be chosen to be the Stone--Cech compactification of $L^*\setminus\{0\}$, where $L^*\setminus\{0\}$ is endowed with the supremum norm topology.
%U http://bims.iranjournals.ir/article_1000_77895c4a78751ae5a2b08a3a3f7d20d2.pdf