RT Journal Article
T1 Homogeneous orthogonally additive polynomials on Banach lattices
A1 Llavona, José G.
A1 Benyamini, Yoav
A1 Lassalle, Silvia
AB 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.
PB Oxford University Press
SN 0024-6093
YR 2006
FD 2006
LK https://hdl.handle.net/20.500.14352/50049
UL https://hdl.handle.net/20.500.14352/50049
LA eng
NO R. Aron, C. Boyd, R. Ryan and I. Zalduendo, ‘Zeros of polynomials on Banach spaces: The real story’, Positivity 7 (2003) 285–295.R. Aron, R. Gonzalo and A. Zagorodnyuk, ‘Zeros of real polynomials’, Linear and multilinear algebra 48 (2000) 107–115.T. K. Carne, B. Cole and T. W. Gamelin, ‘A uniform algebra of analytic functions on a Banach space’, Trans. Amer. Math. Soc. 314 (1989) 639–659.S. Dineen, Complex analysis on infinite dimensional spaces, Springer Monogr. Math. (Springer, 1999).L. Drewnowski and W. Orlicz, ‘On representation of orthogonally additive functionals’, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 17 (1969) 167–173.N. Friedman and M. Katz, ‘Additive functionals on Lp spaces’, Canad. J. Math 18 (1966) 1264–1271.M. I. Garrido, J. A. Jaramillo and J. G. lavona, ‘Polynomial topologies on a Banach space’, Topology Appl. 153 (2005) 854–867.N. J. Kalton, N. T. Peck and J. W. Roberts, An F-space sampler (Cambridge University Press, 1984).S. Lassalle and J. G. Llavona, ‘Weak-polynomial convergence on spaces _p and Lp ’, Positivity 8 (2004) 283–296.J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II (Springer, 1977).M. Marcus and V. J. Mizel, ‘Representation theorems for nonlinear disjointly additive functionals and operators on Sobolev spaces’, Trans. Amer. Math. Soc. 228 (1977) 1–45.V. J. Mizel and K. Sundaresan, ‘Representation of vector valued nonlinear functions’, Trans. Amer. Math. Soc. 159 (1971) 111–127.J. Mujica, Complex analysis in Banach spaces, Math. Studies 120 (North-Holland, Amsterdam, 1986).I. P. Natanson, Theory of functions of a real variable, vol. II (Frederick Ungar Publishing Co., New York, 1960).A. Pelczynski, ‘On weakly compact polynomial operators on B-spaces with Dunford-Pettis property’, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 11 (1963) 371–378.A. Pelczynski, ‘A theorem of Dunford–Pettis type for polynomial operators’, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 11 (1963) 379–386.D. Pérez-García and I. Villanueva, ‘Orthogonally additive polynomials on spaces of continuous functions’, J. Math. Anal. Appl. 306 (2005) 97–105.A. G. Pinsker, ‘Sur une fonctionnelle dans l’espace de Hilbert’, Dokl. Acad. USSR (N.S.) 20 (1938) 411–414. W. Rudin, Functional analysis (McGraw-Hill, 1973). K. Sundaresan, ‘Geometry of spaces of homogeneous polynomials on Banach lattices’, Applied geometry and discrete mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 4 (Amer. Math. Soc., Providence, RI, 1991) 571–586.
NO Technion Fund for the Promotion of Research
DS Docta Complutense
RD 9 may 2024