Some properties of almost summing operators

In this paper we extend the scope of three important results in linear theory absolutely summing operators. The first one was obtained by Bu and Kranz [4] it asserts that a continuous operator between Banach spaces takes almost unconditionally summable sequences into Cohen strongly q-summable for any q≥2, whenever its adjoint is p-summing some p≥1. second them states operators with hilbertian domain are q-summing (1<p,q<∞), result due to [3]. third Kwapień [8] characterizes isomorphic Hilbert space using 2-summing We will show these maintained replacing hypothesis be summing. also give an example fails every 1≤p<∞.