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embedding normed linear spaces into $c(x)$

m. fakhar, 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. m. r. koushesh, 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. m. raoofi, department of mathematical sciences‎, ‎isfahan university of technology‎, ‎isfahan 84156--83111‎, ‎iran.

Abstract

‎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.

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