Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-30T05:59:54.002Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)