A representation theorem for orthogonally additive polynomials on Riesz spaces

被引：0
作者：
A. Ibort
P. Linares
J. G. Llavona
机构：
[1] Universidad Carlos III de Madrid,Departamento de Matemáticas
[2] Universidad Complutense de Madrid,Departamento de Análisis Matemático, Facultad de Matemáticas
来源：
Revista Matemática Complutense | 2012年 / 25卷
关键词：
Orthogonally additive polynomials; Riesz spaces; 46A40; 46G25; 47B65;
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摘要：
The aim of this article is to prove a representation theorem for orthogonally additive polynomials in the spirit of the recent theorem on representation of orthogonally additive polynomials on Banach lattices but for the setting of Riesz spaces. To this purpose the notion of p-orthosymmetric multilinear form is introduced and it is shown to be equivalent to the orthogonally additive property of the corresponding polynomial. Then the space of positive orthogonally additive polynomials on an Archimedean Riesz space taking values on an uniformly complete Archimedean Riesz space is shown to be isomorphic to the space of positive linear forms on the n-power in the sense of Boulabiar and Buskes of the original Riesz space.
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页码：21 / 30
页数：9
相关论文
共 21 条
  • [1] Benyamini Y.(2006)Homogeneous orthogonally-additive polynomials on Banach lattices Bull. Lond. Math. Soc. 38 459-469
  • [2] Lassalle S.(2006)Vector lattice powers: Commun. Algebra 34 1435-1442
  • [3] Llavona J.G.(2007)-algebras and functional calculus Vladikavkaz Math. J. 9 16-29
  • [4] Boulabiar K.(2000)Representation and extension of orthoregular bilinear operators Positivity 4 227-231
  • [5] Buskes G.(2001)Almost Rocky Mt. J. Math. 31 45-56
  • [6] Buskes G.(2006)-algebras: Commutativity and the Cauchy-Schwarz inequality. Positivity and its applications Integral Equ. Oper. Theory 56 597-602
  • [7] Kusraev A.G.(2005)Squares of Riesz spaces Proc. Am. Math. Soc. 133 1083-1091
  • [8] Buskes G.(2009)Orthogonally additive polynomials over Publ. Res. Inst. Math. Sci. 45 519-524
  • [9] van Rooij A.(2005)( J. Math. Anal. Appl. 306 97-105
  • [10] Buskes G.(undefined)) are measures—a short proof undefined undefined undefined-undefined
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