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Journal of Functional Analysis 180, 328 346 (2001) James' Theorem Fails for Starlike Bodies
 

Summary: Journal of Functional Analysis 180, 328 346 (2001)
James' Theorem Fails for Starlike Bodies
D. Azagra
Departamento de Analisis Matematico, Facultad de Ciencias Matematicas,
Universidad Complutense, Madrid 28040, Spain; and ,
Universite Pierre et Marie Curie Paris 6, 4, place Jussieu,
75005 Paris, France
and
R. Deville
Universite Bordeaux I, 351, cours de la Liberation, 33405 Talence cedex, France
E-mail: danielÄsunam1.mat.ucm.es, devilleÄmath.u-bordeaux.fr
Communicated by H. Brezis
Received October 28, 1999; revised August 29, 2000; accepted October 5, 2000
Starlike bodies are interesting in nonlinear functional analysis because they are
strongly related to bump functions and to n-homogeneous polynomials on Banach
spaces, and their geometrical properties are thus worth studying. In this paper we
deal with the question whether James' theorem on the characterization of reflexivity
holds for (smooth) starlike bodies, and we establish that a feeble form of this result
is trivially true for starlike bodies in nonreflexive Banach spaces, but a reasonable
strong version of James' theorem for starlike bodies is never true, even in the smooth

  

Source: Azagra Rueda, Daniel - Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid

 

Collections: Mathematics