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

 

Scalar-valued dominated polynomials on Banach spaces


Authors: Geraldo Botelho and Daniel M. Pellegrino
Journal: Proc. Amer. Math. Soc. 134 (2006), 1743-1751
MSC (2000): Primary 46G25; Secondary 47B10
Published electronically: December 20, 2005
MathSciNet review: 2204287
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Abstract: It is well known that 2-homogeneous polynomials on $ {\mathcal L}_\infty$-spaces are 2-dominated. Motivated by the fact that related coincidence results are possible only for polynomials defined on symmetrically regular spaces, we investigate the situation in several classes of symmetrically regular spaces. We prove a number of non-coincidence results which makes us suspect that there is no infinite dimensional Banach space $ E$ such that every scalar-valued homogeneous polynomial on $ E$ is $ r$-dominated for every $ r \geq 1$.


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Additional Information

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

Daniel M. Pellegrino
Affiliation: Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, 58.109-970, Campina Grande Brazil
Email: pellegrino@dme.ufcg.edu.br

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08501-1
PII: S 0002-9939(05)08501-1
Received by editor(s): January 18, 2005
Published electronically: December 20, 2005
Additional Notes: The authors were partially supported by Instituto do Milênio, IMPA. The second author was also supported by CNPq/FAPESQ
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.