Geodesic
On Isomorphisms of L1 Spaces of Analytic Functions Onto L1
Publications de l'Institut Mathématique, _N_S_50 (1991) no. 64, p. 131

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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},
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     year = {1991},
     language = {en},
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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/