Rosenthal'in l^1-teoremi üzerine

Let X be a Banach space and (x_n)_n be a bounded sequence in X. The sequence (x_n)_n is said to be weakly Cauchy if, for each f in the continuous dual space of X , the sequence (f(x_n))_n converges. In 1974, Haskell P. Rosenthal [10] proved that a Banach space X does not contain an isomorphic copy of l^1 if and only if every bounded sequence (x_n)_n in X has a weakly Cauchy subsequence. In this thesis, we give combinatorial and topological proofs of this theorem and examine some of its equivalences. Then we present some applications of it.