Llavona, José G. and Benyamini, Yoav and Lassalle, Silvia (2006) Homogeneous orthogonally additive polynomials on Banach lattices. Bulletin of the London Mathematical Society , 38 . pp. 459-469. ISSN 0024-6093
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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.
|Uncontrolled Keywords:||Orthogonally additive polynomials; Banach lattices; Weak polynomial convergence|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
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|Deposited On:||12 Jul 2012 13:29|
|Last Modified:||06 Nov 2013 18:22|
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