HOMOGENEOUS ORTHOGONALLY ADDITIVE POLYNOMIALS ON BANACH LATTICES
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)
46G25; 46B42; 47B38.
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.