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Bulletin of the London Mathematical Society Advance Access originally published online on August 13, 2009
Bulletin of the London Mathematical Society 2009 41(5):831-840; doi:10.1112/blms/bdp059
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© 2009 London Mathematical Society

Unconditional bases and strictly convex dual renormings

Richard J. Smith

Institute of Mathematics
Czech Academy of Sciences
Zitná 25
CZ-115 67 Praha 1
Czech Republic

Stanimir Troyanski

Departamento de Matemáticas
Universidad de Murcia
Campus de Espinardo
30100 Murcia
Spain
stroya@um.es

Received 16 December 2008.

We present equivalent conditions for a space X with an unconditional basis to admit an equivalent norm with a strictly convex dual norm.

2000 Mathematics Subject Classification 46B03, 46B26, 46B15.

The first-named author was supported by Grant A 100190801, GA CR 201/07/0394 and the Institute of Mathematics, Czech Academy of Sciences, Institutional Research Plan AV0Z10190503. The second-named author was supported by MTM 2008-05396/MTM/Fondos FEDER, Fundación Séneca 0690/PI/04 CARM, the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgarian National Fund for Scientific Research contract DO 02-360/2008, and by the Center for Advanced Studies at Ben-Gurion University of the Negev.


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