c-Continuous polynomials on l1
DOI:
https://doi.org/10.17398/Palabras clave:
Polynomials, Banach, holomorphic, weakResumen
In this article we study the n-homogeneous polynomials P that are c-continuous on bounded subsets of l1 . We show that P can be decomposed in the form R + Q, where Q and R are n-homogeneous polynomials, with R weakly star continuous and Q (x) = 0 for all x ∈ ker u for u = (1, 1, . . . , 1, . . . ). We conclude that P = Σ un−j ⊗ Rj , where R is a weakly star continuous j-homogeneous polynomial for j = 0, 1, . . . , n.
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R.M. Aron, C. Hervés, M. Valdivia, Weakly continuous mappings on Banach spaces, J. Functional Analysis 52 (1983), 189 – 203.
R.M. Aron, C. Herves, Weakly Sequentially Continuous Analytic Functions on a Banach Space, in “Functional analysis, holomorphy and approximation theory, II (Rio de Janeiro, 1981), Notas Mat. 92, North-Holland Math. Stud. 86, North-Holland Publishing Co., Amsterdam, 1984, 23 – 38.
C. Boyd, S. Dineen, P. Rueda, Weakly uniformly continuous holomorphic functions and the approximation property, Indag. Math. 12 (2) (2001), 147 – 156.
H. Carrión, Entire functions on Banach spaces with the U -property, Bull. Lond. Math. Soc. 54 (1) (2022), 126 – 144.
S. Dineen, “Complex analysis on infinite-dimensional spaces”, Springer-Verlag London, Ltd, London, 1999.
S. Dineen, Entire functions on c0 , J. Funct. Anal. 52 (1983), 205 – 218.
N. Dunford, J. Schwartz, “Linear Operators, Part I: General Theory”, Pure Appl. Math. Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958.
M. González, J.M. Gutiérrez, Factorization of weakly continuous holomorphic mappings, Studia Math. 118 (2) (1996), 117 – 133.
J. Mujica, “Complex analysis in Banach spaces”, Notas Mat. 107, North-Holland Math. Stud. 120, North-Holland Publishing Co., Amsterdam, 1986.
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Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.
