Weak-polynomial convergence on spaces lp and Lp

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This paper is concerned with the study of the set P-1 (0), when P varies over all orthogonally additive polynomials on l(p) and L (p) spaces. We apply our results to obtain characterizations of the weak-polynomial topologies associated to this class of polynomials.
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Aron R. and Rueda, P. (1997), A problem concerning zero-subspaces of homogeneous polynomials, Linear Topological Spaces and Complex Analysis 3 20-23. Aron R., Cole, B. and Gamelin, T. (1991), Spectra of algebras of analytic functions on a Banach space, J. Reine Angew. Math., 415 51-93. Aron R., Gonzalo, R. and Zagorodnyuk, A. (2000), Zeros of real polynomials. Linear and Multilinear Algebra 48 107-115. Aron R., Boyd, C., Ryan, R. and Zalduendo, I. Zeros of polynomials on Banach spaces: the real story. To appear in Positivity. Biström, P., Jaramillo, J.A. and Lindström, M. (1998), Polynomial compactness in Banach spaces, Rocky Mountain Journal of Math. 28 1203-1226. Bonic R. and Frampton, J. (1966), Smooth functions on Banach Manifolds, J. Math. Mech. 15 877-898. Carne T.K., Cole, B. and Gamelin, T.W. (1989), A uniform algebra of analytic functions on a Banach space. Trans. Amer. Math. Soc. 314 639-659. Castillo M.F., García, R. and Gonzalo, R. (1999), Banach spaces in which all multilinear forms are weakly sequentially continuous. Studia Math. 136(2) 121-145. Davie A.M. and Gamelin, T.W. (1989), A Theorem of polynomial-star approximation. Trans. Amer. Math. Soc. 106 351-358. Fabián M., Preiss, D. Whitfield, J.H.M. and Zizler, V.E. (1989), Separating polynomials on Banach spaces Quart. J. Math. Oxford (2) 40 409-422. Garrido M. I., J. A. Jaramillo and J. G. Llavona. Polynomial topologies and uniformities, preprint. González M., Gutiérrez, J.M. and Llavona, J.G. (1997), Polynomial continuity on 1, Proc. Amer. Math. Soc. 125(5) 1349-1353. Gutiérrez J.M. and Llavona, J.G. (1997), Polynomially continuous operators, Israel J. Math. 102 179-187. Lindenstrauss, J. and Tzafriri, L. (1977), Classical Banach Spaces II, Springer, Berlin. Llavona J.G. (1986), Approximation of Continuously Differentiable Functions. North Holland, Amsterdam, Mathematics Studies, 130. Pelczy ski, A. (1957), A property of multilinear operations, Studia Math. 16 173-182. Royden, H.L. (1988), Real Analysis. 3rd Edition, Collier Macmillan. Sundaresan, K. (1991), Geometry of spaces of homogeneous polynomials on Banach lattices. Applied Geometry and Discrete Mathematics 571-586, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 4, Amer. Math. Soc., Prov., RI.