banach spaces - Closed, complemented subspaces of $l^1(X)$ when $X$ is uncountable

A proof in English (modulo some details involving the Pelczynski decomposition method) can be found in the article 'On relatively disjoint families of measures' (Studia Math, 37, p.28-29) by Haskell Rosenthal.

Regarding the analogous result for $ell_p (X)$ ($pin (1,infty)$) and $c_0 (X)$, I seem to recall reading somewhere that it was solved by Joram Lindenstrauss, but now I can't seem to find any reference to it. I seem to think that I saw something about it in the Appendix to the English translation of Banach's book on linear operations (the appendix is by Bessaga and Pelczynski), but it would take me a while to sift through it to find it, and family dinner is being dished up very shortly. I wonder anyhow how much can be gleaned from Matthew Daws' classification of the closed, two-sided ideals in $mathcal{B}(ell_p (X))$, the Banach algebra of all bounded linear operators on $ell_p (X)$? The relevant paper can be downloaded at http://www.amsta.leeds.ac.uk/~mdaws/pubs/ideals.pdf . The paper 'The lattice of closed ideals in the Banach algebra of operators on a certain dual Banach space' by Laustsen, Schlumprecht and Zsak illustrates how classification of the complemented subspaces of a Banach space $E$ can follow from the classification of closed, two-sided ideals in $mathcal{B}(E)$ if all the closed, two-sided ideals are generated by projections onto complemented subspaces having certain nice properties. How much of this can be done using Matt's results I haven't checked, but I think that at the very least some partial results could be obtained. Matt might comment of this if he passes by, or if no one else does I might try to look into it in the next day or so and edit this answer accordingly.

The analogous result for $ell_infty (X)$ does not hold for uncountable $X$ in general. Indeed, every $ell_infty (X)$ is the dual of $ell_1 (X)$, every Banach space embeds isomorphically into some $ell_infty (X)$, but there are injective Banach spaces that are not isomorphic to any dual Banach space; the first such example seems to have been found by Haskell Rosenthal in his paper 'On injective Banach spaces and the spaces $L^infty (mu)$ for finite measure $mu$' (Acta Mathematica, 124, Corollary 4.4), and the existence of such a space provides the desired counterexample.