SAT-320 Characteristic of the dual space of l^(infinity)

Saturday, October 13, 2012: 7:20 AM
Hall 4E/F (WSCC)
Raghda Abouelnaga , Mathematics, University of California, Berkeley, Antioch, CA
Santigo Canez, PhD , Mathematics, University of California, Berkeley, Berkeley
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