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    Kusraeva, Z. A. 2016. On compact domination of homogeneous orthogonally additive polynomials. Siberian Mathematical Journal, Vol. 57, Issue. 3, p. 519.


    Alaminos, J. Extremera, J. and Villena, A.R. 2015. Orthogonally additive polynomials on Fourier algebras. Journal of Mathematical Analysis and Applications, Vol. 422, Issue. 1, p. 72.


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    Ibort, A. Linares, P. and Llavona, J. G. 2012. A representation theorem for orthogonally additive polynomials on Riesz spaces. Revista Matemática Complutense, Vol. 25, Issue. 1, p. 21.


    Jaramillo, Jesús Ángel Prieto, Ángeles and Zalduendo, Ignacio 2012. Orthogonally additive holomorphic functions on open subsets of C(K). Revista Matemática Complutense, Vol. 25, Issue. 1, p. 31.


    Kusraeva, Z. A. 2012. Homogeneous orthogonally additive polynomials on vector lattices. Mathematical Notes, Vol. 91, Issue. 5-6, p. 657.


    Кусраева, Залина Анатольевна and Kusraeva, Zalina Anatoljevna 2012. Однородные ортогонально аддитивные полиномы в векторных решетках. Математические заметки, Vol. 91, Issue. 5, p. 704.


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    Toumi, Mohamed Ali 2011. ORTHOGONALLY ADDITIVE POLYNOMIALS ON DEDEKIND σ-COMPLETE VECTOR LATTICES. Mathematical Proceedings of the Royal Irish Academy, Vol. 110, Issue. -1, p. 83.


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  • Bulletin of the London Mathematical Society, Volume 38, Issue 3
  • June 2006, pp. 459-469

HOMOGENEOUS ORTHOGONALLY ADDITIVE POLYNOMIALS ON BANACH LATTICES

  • YOAV BENYAMINI (a1), SILVIA LASSALLE (a2) and JOSÉ G. LLAVONA (a3)
  • DOI: http://dx.doi.org/10.1112/S0024609306018364
  • Published online: 01 May 2006
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.

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Bulletin of the London Mathematical Society
  • ISSN: 0024-6093
  • EISSN: 1469-2120
  • URL: /core/journals/bulletin-of-the-london-mathematical-society
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