RT Journal Article
T1 Local complementation and the extension of bilinear mappings
A1 Castillo, J.M.F.
A1 García, R.
A1 Defant, A.
A1 Pérez García, David
A1 Suárez, J.
AB 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 Aron-Berner 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 Lindenstrauss-Pelczynski and Johnson-Zippin theorems fail. We will then consider the notion of locally alpha-complemented subspace for a reasonable tensor norm alpha, and study the connections between alpha-local complementation and the extendability of alpha* -integral operators.
PB Cambridge Phylosophical Society
SN 0305-0041
YR 2012
FD 2012-01
LK https://hdl.handle.net/20.500.14352/42455
UL https://hdl.handle.net/20.500.14352/42455
LA eng
NO Junta de Extremadura. IV Plan Regional I+D+I, Ayudas a Grupos de Investigación
DS Docta Complutense
RD 7 jul 2025