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P-continuity on classical Banach spaces

Llavona, José G. and Hájek, P. (2000) P-continuity on classical Banach spaces. Proceedings of the American Mathematical Society, 128 ( 3). 827-830 . ISSN 0002-9939

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Abstract

Given a Banach space X and an integer n, the existence of an n-homogeneous polynomial which is not uniformly continuous with respect to the polynomial topology on B-X is investigated. We provide a complete characterization for some classical Banach spaces, while for others a surprising unresolved difficulty is encountered for a certain value of n (depending on X).

Item Type:Article
Uncontrolled Keywords:P-continuity
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16007
References:

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

J. Diestel, Sequences and series in Banach spaces, Grad. Texts in Math. 92, Springer, Berlin, 1984.

J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Univ. Press, 1996.

M. González, J. M. Gutiérrez and J. G. Llavona, Polynomial continuity on1, Proc. Amer. Math. Soc. 125, no. 5 (1997), 1349–1353.

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

Deposited On:20 Jul 2012 10:34
Last Modified:06 Feb 2014 10:36

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