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Castillo, J.M.F. and García, R. and Defant, A. and Pérez García, David and Suárez, J. (2012) Local complementation and the extension of bilinear mappings. Mathematical Proceedings of the Cambridge Philosophical Society, 152 (1). pp. 153166. ISSN 03050041
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Official URL: http://journals.cambridge.org/abstract_S0305004111000533
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http://jwww.cambridge.org/  UNSPECIFIED 
Abstract
We study different aspects of the connections between local theory of Banach spaces and the problem of the extension of bilinear forms from subspaces of Banach spaces. Among other results, we prove that if X is not a Hilbert space then one may find a subspace of X for which there is no AronBerner extension. We also obtain that the extension of bilinear forms from all the subspaces of a given X forces such X to contain no uniform copies of l(p)(n) for p is an element of [1, 2). In particular, X must have type 2  epsilon for every epsilon > 0. Also, we show that the bilinear version of the LindenstraussPelczynski and JohnsonZippin theorems fail. We will then consider the notion of locally alphacomplemented subspace for a reasonable tensor norm alpha, and study the connections between alphalocal complementation and the extendability of alpha* integral operators.
Item Type:  Article 

Uncontrolled Keywords:  HahnBanach theorem for bilinear forms; local complementation 
Subjects:  Sciences > Mathematics > Functional analysis and Operator theory 
ID Code:  17517 
Deposited On:  20 Dec 2012 11:13 
Last Modified:  03 Dec 2014 11:51 
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