  We study the ideals of linear operators between Banach spaces determined by
the transformation of vector-valued sequences involving the new sequence space
introduced by Karn and Sinha \cite{karnsinha} and the classical spaces of
absolutely, weakly and Cohen strongly summable sequences. As applications, we
prove a new factorization theorem for absolutely summing operators and a
contribution to the existence of infinite dimensional spaces formed by
non-absolutely summing operators is given.
