Let X be a Banach space and let Y be a separable Lindenstrauss space. We describe the Banach space P (Y, X) of absolutely summing operators as a general L1-tree space. We also characterize the bounded APPROXIMATION PROPERTY and its weak version for X in terms of the space of integral operators I (X, Z*) and the space of nuclear operators N (X, Z*), respectively, where Z is a Lindenstrauss space, whose dual Z* fails to have the Radon-Nikod´ym PROPERTY.