PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 50(64) Preimenovati datoteke, proveriti paginaciju!!!, pp. 131134 (1991) 

On isomorphisms of $L^1$ spaces of analytic functions onto $l^1$Miroslav Pavlovi{\cj}Matematicki fakultet, Beograd, YugoslaviaAbstract: It is proved that an $L^1_{\f}$ space of analytic functions in the unit disc, with the weight $\f'(1z)$, is isomorphic to the Lebesgue sequence space $l^1$ only if $\f$ is ``normal''. The converse is known from the papers of Shields and Williams [{\bf 13}] and Lindenstrauss and Pelczynski [{\bf 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 LindenstraussPelczynski's theorem on the equivalence of unconditional bases in $l^1$. Classification (MSC2000): 46E15, 46B20 Full text of the article:
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