TY - JOUR ID - 1000 TI - Embedding normed linear spaces into $C(X)$ JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Fakhar, M. AU - Koushesh, M. R. AU - Raoofi, M. AD - Department of Mathematics‎, ‎University of Isfahan‎, ‎Isfahan 81745--163‎, ‎Iran‎, ‎and‎, ‎School of Mathematics‎, ‎Institute for Research in Fundamental Sciences (IPM)‎, ‎P.O‎. ‎Box: ‎19395--5746‎, ‎Tehran‎, ‎Iran. AD - Department of Mathematical Sciences‎, ‎Isfahan University of Technology‎, ‎Isfahan 84156--83111‎, ‎Iran‎, ‎and‎, ‎School of Mathematics‎, ‎Institute for Research in Fundamental Sciences (IPM)‎, ‎P.O‎. ‎Box‎: ‎19395--5746‎, ‎Tehran‎, ‎Iran. AD - Department of Mathematical Sciences‎, ‎Isfahan University of Technology‎, ‎Isfahan 84156--83111‎, ‎Iran. Y1 - 2017 PY - 2017 VL - 43 IS - 1 SP - 131 EP - 135 KW - Stone-Cech compactification KW - Banach-Alaoglu theorem KW - embedding theorem DO - N2 - ‎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. UR - http://bims.iranjournals.ir/article_1000.html L1 - http://bims.iranjournals.ir/article_1000_77895c4a78751ae5a2b08a3a3f7d20d2.pdf ER -