Title of article
Embedding normed linear spaces into $C(X)$
Author/Authors
-، - نويسنده Department of Mathematics, University of Isfahan, Isfahan 81745--163, Iran, and, School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: Fakhar, M. , -، - نويسنده Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156--83111, Iran, and, School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Koushesh, M. R. , -، - نويسنده Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156--83111, Iran. Raoofi, M.
Issue Information
دوماهنامه با شماره پیاپی 0 سال 2017
Pages
5
From page
131
To page
135
Abstract
-
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.
Journal title
Bulletin of the Iranian Mathematical Society
Journal title
Bulletin of the Iranian Mathematical Society
Record number
2400328
Link To Document