Characteristic of the dual space of l^(infinity)

The purpose of our research was to find the characterization of dual space of l(infinity) –The set of all bounded sequences –avoiding the usage of  measure theory.  We found that a simpler representation will be the sum of l^1+ the annihilator of C_o.  The paper show the proof in details: First we constructed a bijective map between l^infinity and the direct sum of Null C_o and l^1, and the since it was proven already that l(1) is isomorphic to the dual of C_o so it was enough to construct an equivalent bijective function between the dual of l (infinity) and the sum of  the dual of C_0 and the annihilator of C_o. The importance of this new equivalent map was to give a clear reasoning on how norms are preserved since C_o dual and the annihilator of C_o both represent functions so their sum also represents functions . This raised another question about the existence of a well defined 0 map from C_0 to 0 with the form G: C_0 →aX such that “a” is a vector in the orthogonal space of C_0