On The Second Dual of the Space of Continuous Functions

Samuel Kaplan
1957 Transactions of the American Mathematical Society  
Introduction. By "the space of continuous functions" we mean the Banach space C of real continuous functions on a compact Hausdorff space X. C, its first dual, and its second dual are not only Banach spaces, but also vector lattices, and this aspect of them plays a central role in our treatment. In § §1-3, we collect the properties of vector lattices which we need in the paper. In §4 we add some properties of the first dual of C-the space of Radon measures on X-denoted by L in the present
more » ... n the present paper. In §5 we imbed C in its second dual, denoted by M, and then identify the space of all bounded real functions on X with a quotient space of M, in fact with a topological direct summand. Thus each bounded function on X represents an entire class of
doi:10.2307/1992866 fatcat:e56j7txavbfudkehl27ppu4jsq