The GL-l.u.st. constant and asymmetry of the Kalton-Peck twisted sum in finite dimensions

Authors:
Y. Gordon, M. Junge, M. Meyer and S. Reisner

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2793-2805

MSC (2010):
Primary 46B20; Secondary 46B07

Published electronically:
February 22, 2011

MathSciNet review:
2801620

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Abstract: We prove that the Kalton-Peck twisted sum of -dimensional Hilbert spaces has a GL-l.u.st. constant of order and bounded GL constant. This is the first concrete example which shows different explicit orders of growth in the GL and GL-l.u.st. constants. We also discuss the asymmetry constants of .

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Additional Information

**Y. Gordon**

Affiliation:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel

Email:
gordon@techunix.technion.ac.il

**M. Junge**

Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801

Email:
junge@math.uiuc.edu

**M. Meyer**

Affiliation:
Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), Université Paris-Est-Marne-la-Vallée, Cité Descartes-5, Bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France

Email:
Mathieu.Meyer@univ-mlv.fr

**S. Reisner**

Affiliation:
Department of Mathematics, University of Haifa, Haifa 31905, Israel

Email:
reisner@math.haifa.ac.il

DOI:
https://doi.org/10.1090/S0002-9939-2011-10715-9

Keywords:
Banach spaces,
local unconditional structure,
asymmetry

Received by editor(s):
March 12, 2010

Received by editor(s) in revised form:
July 21, 2010

Published electronically:
February 22, 2011

Additional Notes:
The first, third and fourth authors were supported in part by the France-Israel Research Network Program in Mathematics contract #3-4301.

The second author was supported in part by NSF grant DMS-0901457.

Dedicated:
Dedicated to the memory of Nigel J. Kalton

Communicated by:
Nigel J. Kalton

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.