Preprint No. A-03-10

Vladimir Kadets, Nigel Kalton, Dirk Werner

Unconditionally convergent series of operators and narrow operators on $L_1$

Abstract: We introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$ into a space with an unconditional basis belongs to this class.

Keywords: Banach spaces, narrow operators, unconditional convergence, unconditional bases

Mathematics Subject Classification (MSC2000): 46B04; 46B15, 46B25, 47B07

Language: ENG


Contact: Dirk Werner, Freie Universität Berlin, Fachbereich Mathematik und I nformatik, Arnimallee 2-6, D-14195 Berlin, Germany (

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