Bulletin of the London Mathematical Society



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HOMOGENEOUS ORTHOGONALLY ADDITIVE POLYNOMIALS ON BANACH LATTICES


YOAV BENYAMINI a1 1 , SILVIA LASSALLE a2 1 and JOSÉ G. LLAVONA a3 1
a1 Department of Mathematics, Technion — Israel Institute of Technology, Haifa 32000, Israel yoavb@tx.technion.ac.il
a2 Departamento de Matemática — PAB I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina slassall@dm.uba.ar
a3 Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain JL_Llavona@mat.ucm.es

Article author query
benyamini y   [Google Scholar] 
lassalle s   [Google Scholar] 
llavona jg   [Google Scholar] 
 

Abstract

The main result in this paper is a representation theorem for homogeneous orthogonally additive polynomials on Banach lattices. The representation theorem is used to study the linear span of the set of zeros of homogeneous real-valued orthogonally additive polynomials. It is shown that in certain lattices every element can be represented as the sum of two or three zeros or, at least, can be approximated by such sums. It is also indicated how these results can be used to study weak topologies induced by orthogonally additive polynomials on Banach lattices.

(Received April 22 2004)
(Revised March 31 2005)

Maths Classification

46G25; 46B42; 47B38.



Footnotes

1 The research of the first author was supported by the Technion Fund for the Promotion of Research, the second author was partially supported by UBACyT X108 and PICT03-15033, and the third author was supported in part by Project BFM2000-0609.