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The 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 | References | Similar Articles | Additional Information

Abstract: We prove that the Kalton-Peck twisted sum $ Z_2^n$ of $ n$-dimensional Hilbert spaces has a constant of order $ \log n$ and bounded GL constant. This is the first concrete example which shows different explicit orders of growth in the GL and constants. We also discuss the asymmetry constants of $ Z_2^n$.

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Additional Information

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

M. Junge
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801

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

S. Reisner
Affiliation: Department of Mathematics, University of Haifa, Haifa 31905, Israel

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.

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