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