Llavona, José G. and Linares Briones, Pablo and Ibort Latre, Luis Alberto
(2009)
*On the Representation of Orthogonally Additive Polynomials in l(p).*
Publications of the Research Institute for Mathematical Sciences, 45
(2).
519 -524 .
ISSN 0034-5318

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## Abstract

We present a new proof of a Sundaresan's result which shows that the space of orthogonally additive polynomials P-0((k)l(p)) is isometrically isomorphic to l(p/p-k) if k < p < infinity and to l(infinity) if 1 <= p <= k.

Item Type: | Article |
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Uncontrolled Keywords: | Orthogonally additive polynomials; Tensor diagonal |

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

ID Code: | 15897 |

References: | R. M. Aron and J. Globevnik, Analytic functions on c0, Rev. Mat. Univ. Complut. Madrid 2 (1989), suppl., 27–33. Y. Benyamini, S. Lassalle and J. G. Llavona, Homogeneous orthogonally additive polynomials on Banach lattices, Bull. London Math. Soc. 38 (2006), no. 3, 459–469. D. Carando, S. Lassalle and I. Zalduendo, Orthogonally additive polynomials over C(K) are measures—a short proof, Integral Equations Operator Theory 56 (2006), no. 4, 597– 602. S. Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer, London, 1999. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. II, Springer, Berlin, 1979. [6] J. Mujica, Complex analysis in Banach spaces, North-Holland, Math. Studies, 120, Amsterdam, 1986. D. Pérez-García and I. Villanueva, Orthogonally additive polynomials on spaces of continuous functions, J. Math. Anal. Appl. 306 (2005), no. 1, 97–105. R. A. Ryan, Introduction to tensor products of Banach spaces, Springer, London, 2002. K. Sundaresan, Geometry of spaces of homogeneous polynomials on Banach lattices, in Applied geometry and discrete Mathematics, 571–586, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 4, Amer. Math. Soc., Providence, RI, 1991. I. Zalduendo, An estimate for multilinear forms on _p spaces, Proc. Roy. Irish Acad. Sect. A 93 (1993), no. 1, 137–142. |

Deposited On: | 11 Jul 2012 07:43 |

Last Modified: | 06 Feb 2014 10:34 |

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