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Bulletin of the London Mathematical Society 2005 37(2):265-274; doi:10.1112/S0024609304003881
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© London Mathematical Society

Unconditionally Convergent Series of Operators and Narrow Operators on L1

Vladimir Kadets, Nigel Kalton and Dirk Werner

Faculty of Mechanics and Mathematics, Kharkov National University pl. Svobody 4, 61077 Kharkov, Ukraine vova1kadets{at}yahoo.com
Department of Mathematics, University of Missouri Columbia, MO 65211, USA nigel{at}math.missouri.edu
Department of Mathematics, Freie Universität Berlin Arnimallee 2–6, D-14 195 Berlin, Germany werner{at}math.fu-berlin.de

Received 17 November 2003.

A class of operators is introduced on L1 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 L1 into a space with an unconditional basis belongs to this class. 2000 Mathematics Subject Classification 46B04 (primary), 46B15, 46B25, 47B07 (secondary).

The work of the first author was supported by a fellowship from the Alexander-von-Humboldt Stiftung.

The second author was supported by NSF grant DMS-9870027.


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