Llavona, José G. and Ibort Latre, Luis Alberto and Linares Briones, Pablo
(2012)
*A representation theorem for orthogonally additive polynomials on Riesz spaces.*
Revista matemática complutense, 25
(1).
21-30 .
ISSN 1139-1138

PDF
Restringido a Repository staff only hasta 31 December 2020. 398kB |

Official URL: http://www.springerlink.com/content/p328874m514780v0/fulltext.pdf

## Abstract

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.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Orthogonally additive polynomials; Riesz spaces |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 15845 |

References: | Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Springer, Berlin (2006) Benyamini, Y., Lassalle, S., Llavona, J.G.: Homogeneous orthogonally-additive polynomials on Banach lattices. Bull. Lond. Math. Soc. 38, 459–469 (2006) Boulabiar, K., Buskes, G.: Vector lattice powers: f-algebras and functional calculus. Commun. Algebra 34(4), 1435–1442 (2006) Buskes, G., Kusraev, A.G.: Representation and extension of orthoregular bilinear operators. Vladikavkaz Math. J. 9(1), 16–29 (2007) Buskes, G., van Rooij, A.: Almost f-algebras: Commutativity and the Cauchy-Schwarz inequality. Positivity and its applications. Positivity 4(3), 227–231 (2000) Buskes, G., van Rooij, A.: Squares of Riesz spaces. Rocky Mt. J. Math. 31(1), 45–56 (2001) Carando, D., Lassalle, S., Zalduendo, I.: Orthogonally additive polynomials over C(K) are measures—a short proof. Integral Equ. Oper. Theory 56(4), 597–602 (2006) Grecu, B., Ryan, R.A.: Polynomials on Banach spaces with unconditional bases. Proc. Am. Math. Soc. 133(4), 1083–1091 (2005) Ibort, A., Linares, P., Llavona, J.G.: On the representation of orthogonally additive polynomials in ℓ p . Publ. Res. Inst. Math. Sci. 45(2), 519–524 (2009) de Jonge, E., van Rooij, A.: Introduction to Riesz Spaces. Mathematical Centre Tracts, vol. 78. Mathematisch Centrum, Amsterdam (1977) Pérez García, D., Villanueva, I.: Orthogonally additive polynomials on spaces of continuous functions. J. Math. Anal. Appl. 306, 97–105 (2005) Toumi, M.A.: A decomposition theorem for orthogonally additive polynomials on Archimedean vector lattices. Private communication (2010) |

Deposited On: | 06 Jul 2012 09:16 |

Last Modified: | 06 Feb 2014 10:32 |

Repository Staff Only: item control page