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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Inclusions and coincidences for multiple summing multilinear mappings


Authors: G. Botelho, H.-A. Braunss, H. Junek and D. Pellegrino
Journal: Proc. Amer. Math. Soc. 137 (2009), 991-1000
MSC (2000): Primary 46G25
Published electronically: October 8, 2008
MathSciNet review: 2457439
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Abstract: Using complex interpolation we prove new inclusion and coincidence theorems for multiple (fully) summing multilinear and holomorphic mappings. Among several other results we show that continuous $ n$-linear forms on cotype 2 spaces are multiple $ (2;q_{k},...,q_{k})$-summing, where $ 2^{k-1}<n\leq2^{k}$, $ q_{0}=2$ and $ q_{k+1}=\frac{2q_{k}}{1+q_{k}}$ for $ k\geq0.$


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Additional Information

G. Botelho
Affiliation: Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902, Uberlândia, Brazil
Email: botelho@ufu.br

H.-A. Braunss
Affiliation: Institute of Mathematics, University of Potsdam, 14469, Potsdam, Germany
Email: braunss@rz.uni-potsdam.de

H. Junek
Affiliation: Institute of Mathematics, University of Potsdam, 14469, Potsdam, Germany
Email: junek@rz.uni-potsdam.de

D. Pellegrino
Affiliation: Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, J. Pessoa, PB, Brazil
Email: pellegrino.math@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09691-3
PII: S 0002-9939(08)09691-3
Received by editor(s): March 4, 2008
Published electronically: October 8, 2008
Additional Notes: The fourth author is supported by CNPq Grant 308084/2006-3 and Edital MCT/CNPq 02/2006-Universal, Grant 471054/2006-2
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.