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Homogeneous Orthogonally Additive Polynomials on Banach Lattices |
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| Authors: | Benyamini Yoav; Lassalle Silvia; Llavona Jose G |
| Institution: | Department of Mathematics, Technion — Israel Institute of Technology Haifa 32000, Israel; yoavb{at}tx.technion.ac.il Departamento de Matemática — PAB I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires (1428) Buenos Aires, Argentina; slassall{at}dm.uba.ar Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid 28040 Madrid, Spain; JL_Llavona{at}mat.ucm.es |
| Abstract: | The main result in this paper is a representation theorem forhomogeneous orthogonally additive polynomials on Banach lattices.The representation theorem is used to study the linear spanof the set of zeros of homogeneous real-valued orthogonallyadditive polynomials. It is shown that in certain lattices everyelement can be represented as the sum of two or three zerosor, at least, can be approximated by such sums. It is also indicatedhow these results can be used to study weak topologies inducedby orthogonally additive polynomials on Banach lattices. 2000Mathematics Subject Classification 46G25, 46B42, 47B38. |
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