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HOMOGENEOUS ORTHOGONALLY ADDITIVE POLYNOMIALS ON BANACH LATTICES

Published online by Cambridge University Press:  31 May 2006

YOAV BENYAMINI ,
SILVIA LASSALLE  and
JOSÉ G. LLAVONA
YOAV BENYAMINI
Affiliation:
Department of Mathematics, Technion — Israel Institute of Technology, Haifa 32000, Israelyoavb@tx.technion.ac.il
SILVIA LASSALLE
Affiliation:
Departamento de Matemática — PAB I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentinaslassall@dm.uba.ar
JOSÉ G. LLAVONA
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, SpainJL_Llavona@mat.ucm.es
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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.

Keywords

46G2546B4247B38
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 3 , June 2006 , pp. 459 - 469
Copyright
© The London Mathematical Society 2006

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