Title of article :
Embedding normed linear spaces into C(X)
Author/Authors :
Fakhar ، M. - University of Isfahan , Koushesh ، M. R. - Isfahan University of Technology , Raoofi ، M. - Isfahan University of Technology
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∗∖{0}, where L∗∖{0} is endowed with the supremum norm topology.
Keywords :
Stone , Cech compacti cation , Banach , Alaoglu theorem , embedding theorem
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
