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Polynomials generated by linear operators

Authors: P. Galindo, M. L. Lourenço and L. A. Moraes
Journal: Proc. Amer. Math. Soc. 132 (2004), 2917-2927
MSC (2000): Primary 46G20
Published electronically: June 2, 2004
MathSciNet review: 2063111
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Abstract: We study the class of Banach algebra-valued $n$-homogeneous polynomials generated by the $n^{th}$ powers of linear operators. We compare it with the finite type polynomials. We introduce a topology $w_{EF}$ on $E,$ similar to the weak topology, to clarify the features of these polynomials.

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Additional Information

P. Galindo
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia 46.100, Burjasot-Valencia, Spain

M. L. Lourenço
Affiliation: Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281 - CEP : 05315-970, São Paulo, Brazil

L. A. Moraes
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, CP 68530 - CEP: 21945-970, Rio de Janeiro, Brazil

Keywords: $n$-homogeneous polynomials, linear operator, Arens product
Received by editor(s): September 4, 2002
Published electronically: June 2, 2004
Additional Notes: The first author was supported by CCInt-USP and FAPEMIG
The second author was supported in part by agreement USP/UV and FAPESP
The third author was supported in part by CNPq, Research Grant 300016/82-4 and PROAP/UFRJ
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2004 American Mathematical Society

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