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Homogeneous Orthogonally Additive Polynomials on Banach Lattices
Author(s) -
Benyamini Yoav,
Lassalle Silvia,
Llavona José G.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018364
Subject(s) - mathematics , homogeneous , representation (politics) , element (criminal law) , pure mathematics , span (engineering) , discrete mathematics , combinatorics , civil engineering , politics , political science , law , engineering
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. 2000 Mathematics Subject Classification 46G25, 46B42, 47B38.