Abstract
We present a homological principle that governs the behaviour of couples of exact sequences of quasi-Banach spaces. Three applications are given: (i) A unifying method of proof for the results of Lindenstrauss, Rosenthal, Kalton, Peck and Kislyakov about the extension and lifting of isomorphisms inc 0,ι ∞,ι p andL pfor 0<p≤1; (ii) A study of the Dunford-Pettis property in duals of quotients ofL ∞-spaces; and (iii) New results on the extension ofC(K)-valued operators.
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The research has been supported in part by DGICYT project BFM 2001-0813.
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Castillo, J.M.F., Moreno, Y. On the Lindenstrauss-Rosenthal theorem. Isr. J. Math. 140, 253–270 (2004). https://doi.org/10.1007/BF02786635
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DOI: https://doi.org/10.1007/BF02786635