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The Aron-Berner extension, Goldstine's theorem and P-continuity


García González, Ricardo y Jaramillo Aguado, Jesús Ángel y Llavona, José G. (2011) The Aron-Berner extension, Goldstine's theorem and P-continuity. Mathematische Nachrichten, 284 (5-6). pp. 694-702. ISSN 0025-584X

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In this paper we show that the Aron-Berner type extension of polynomials preserves the P-continuity property. To this end we introduce a new version of Goldstine's Theorem for locally complemented subspaces.

Tipo de documento:Artículo
Palabras clave:Aron-Berner extension, P-continuity, polynomials, Banach spaces
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:16211

R. Arens, The adjoint of a bilinear operation, Proc. Am. Math. Soc. 2, 839–848 (1951).

R. Aron and P. Berner, A Hahn-Banach extension theorem for analytic mappings, Bull. Soc. Math. Fr. 106(1), 3–24 (1978).

R. Aron, Y. S. Choi, and J. G. Llavona, Estimates by polynomials, Bull. Aust. Math. Soc. 52, 475–486 (1995).

R. Aron, P. Galindo, D. García, and M. Maestre, Regularity and algebras of analytic functions in infinite dimensions, Trans. Am. Math. Soc. 348(2), 543–559 (1996).

F. Cabello and R. García, The bidual of a tensor product of Banach spaces, Rev. Mat. Iberoam. 21(3), 843–861 (2005).

F. Cabello, R. García, and I. Villanueva, Extensions of multilinear operators on Banach spaces, Extr. Math. 15, 291–334 (2000).

D. Carando and S. Lassalle, E_ and its relation with vector-valued functions on E, Ark. Mat. 42, 283–300 (2004).

A. M. Davie and T. W. Gamelin, A theorem on polynomial-star approximation, Proc. Am. Math. Soc. 106, 351–356 (1989).

P. Galindo, D. García, M. Maestre, and J. Mujica, Extensions of multilinear mappings on Banach spaces, Stud. Math. 108, 55–77 (1994).

P. Galindo, M. Maestre, and P. Rueda, Biduality in spaces of holomorphic functions, Math. Scand. 86, 5–16 (2000).

M. González, J. M. Gutiérrez, and J. G. Llavona, Polynomial continuity on l1 , Proc. Am. Math. Soc. 125(5), 1349–1353 (1997)

J. M. Gutiérrez and J. G. Llavona, Polynomially continuous operators, Isr. J. Math. 102, 179–183 (1997).

P. Hajek and J. G. Llavona, P-continuity on classical Banach spaces, Proc. Am. Math. Soc. 128(3), 827–830 (2000).

W. B. Johnson, Extensions of c0 , Positivity 1, 55–74 (1997).

N. J. Kalton, Locally complemented subspaces and Lp -spaces for 0 < p < 1, Math. Nachr. 115, 71–97 (1984).

J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergebnisse der Mathematik und ihrer Grenzgebiete Band 92 (Springer-Verlag, Berl´ın, 1977).

M. Lindstr¨om and R. Ryan, Applications of ultraproducts to infinite dimensional holomorphy, Math. Scand. 71, 229–242 (1992).

J. G. Llavona, Approximation of Continuously Differentiable Functions, North-Holland Mathematics Studies Vol. 130 (North-Holland, Amsterdam, New York, 1986).

J. G. Llavona and L. A.Moraes, The Aron-Berner extension for polynomials defined in the dual of a Banach space, Publ. RIMS, Kyoto Univ. 40, 221–230 (2004).

J. Mujica, Complex Analysis in Banach Spaces, North-Holland Mathematics Studies Vol. 120 (North-Holland, Amsterdam, 1986).

O. Nicodemi, Homomorphisms of Algebras of Germs of Holomorphic Functions, in: Proceedings of the Symposium on Functional Analysis, Holomorphy and Approximation Theory held at the Federal University of Rio de Janeiro, Rio de Janeiro 1978, Lecture Notes in Mathematics Vol. 843 (Springer, Berlin-New York, 1981), pp. 534–546.

I. Zalduendo, A canonical extension for analytic functions on Banach spaces, Trans. Am. Math. Soc. 320, 747–763 (1990).

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