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UNCONDITIONALLY CONVERGENT SERIES OF OPERATORS AND NARROW OPERATORS ON $L_1$

Published online by Cambridge University Press:  10 March 2005

VLADIMIR KADETS ,
NIGEL KALTON  and
DIRK WERNER
VLADIMIR KADETS
Affiliation:
Faculty of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, 61077 Kharkov, Ukrainevova1kadets@yahoo.com
NIGEL KALTON
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USAnigel@math.missouri.edu
DIRK WERNER
Affiliation:
Department of Mathematics, Freie Universität Berlin, Arnimallee 2–6, D-14 195 Berlin, Germanywerner@math.fu-berlin.de
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Abstract

A class of operators is introduced 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

46B04 (primary)46B1546B2547B07 (secondary)

Information

Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 2 , March 2005 , pp. 265 - 274
Copyright
© The London Mathematical Society 2005

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