Geodesic
On Isomorphisms of L1 Spaces of Analytic Functions Onto L1
Publications de l'Institut Mathématique, _N_S_50 (1991) no. 64, p. 131
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It is proved that an $L^1_{\varphi}$ space of analytic functions in the unit disc, with the weight $\varphi'(1-|z|)$, is isomorphic to the Lebesgue sequence space $l^1$ only if $\varphi$ is ``normal''. The converse is known from the papers of Shields and Williams [13] and Lindenstrauss and Pelczynski [4]. The key of our proof are three classical results: Paley's theorem on lacunary series, Pelczynski's theorem on complemented subspaces of $l^1$ and Lindenstrauss-Pelczynski's theorem on the equivalence of unconditional bases in $l^1$.
Classification : 46E15 46B20 
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     author = {Miroslav Pavlovi\'c},
     title = {On {Isomorphisms} of {L1} {Spaces} of {Analytic} {Functions} {Onto} {L1}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {131 },
     year = {1991},
     volume = {_N_S_50},
     number = {64},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1991_N_S_50_64_a15/}
}
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Miroslav Pavlović. On Isomorphisms of L1 Spaces of Analytic Functions Onto L1. Publications de l'Institut Mathématique, _N_S_50 (1991) no. 64, p. 131 . http://geodesic.mathdoc.fr/item/PIM_1991_N_S_50_64_a15/